Problem trying to represent growth of a capital with spirals
I am trying to represent with spirals the growth of a capital as the Bank pays interest.
The analogy would be that the capital is represented by the radius and the passage of time by the motion of the circle with constant angular speed.
The Archimedes spiral (where radius is growing in arithmetic progression) would be the equivalent of simple interest and the logarithmic spiral would represent compound interest.
Going quantitative, I have doubts. I have tried to adapt the formulas as follows (I am stipulating that one turn is 1 year):
SIMPLE INTEREST (Archimides spiral):
$r(theta ) = atheta
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaeqiUdeha
% aa!3DBF!
$
would become
$r(theta )[{rm{final capital}}] = {rm{initial capital + a[yearly interest]}}frac{theta }{{2pi }}{rm{[fraction or multiple of year elapsed]}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaGGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaac2facqGH9aqpcaqGPbGaaeOBaiaabMgacaqG
% 0bGaaeyAaiaabggacaqGSbGaaeiiaiaabogacaqGHbGaaeiCaiaabM
% gacaqG0bGaaeyyaiaabYgacaqGRaGaaeyyaiaabUfacaqG5bGaaeyz
% aiaabggacaqGYbGaaeiBaiaabMhacaqGGaGaaeyAaiaab6gacaqG0b
% GaaeyzaiaabkhacaqGLbGaae4CaiaabshacaqGDbWaaSaaaeaacqaH
% 4oqCaeaacaaIYaGaeqiWdahaaiaabUfacaqGMbGaaeOCaiaabggaca
% qGJbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaqGVbGaaeOCaiaa
% bccacaqGTbGaaeyDaiaabYgacaqG0bGaaeyAaiaabchacaqGSbGaae
% yzaiaabccacaqGVbGaaeOzaiaabccacaqG5bGaaeyzaiaabggacaqG
% YbGaaeiiaiaabwgacaqGSbGaaeyyaiaabchacaqGZbGaaeyzaiaabs
% gacaqGDbaaaa!8D58!
$
COMPOUND INTEREST (Logarithmic spiral):
$r(theta ) = a{e^{theta b}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaamyzamaa
% CaaaleqabaGaeqiUdeNaamOyaaaaaaa!3FBD!
$
would become
$r(theta ){rm{[final capital]}} = a[{rm{initial capital]}}{e^{b[{rm{yearly interest rate]}}frac{theta }{{2pi }}[{rm{fraction or multiple of year elapsed]}}}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaqGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaab2facqGH9aqpcaWGHbGaai4waiaabMgacaqG
% UbGaaeyAaiaabshacaqGPbGaaeyyaiaabYgacaqGGaGaae4yaiaabg
% gacaqGWbGaaeyAaiaabshacaqGHbGaaeiBaiaab2facaWGLbWaaWba
% aSqabeaacaWGIbGaai4waiaabMhacaqGLbGaaeyyaiaabkhacaqGSb
% GaaeyEaiaabccacaqGPbGaaeOBaiaabshacaqGLbGaaeOCaiaabwga
% caqGZbGaaeiDaiaabccacaqGYbGaaeyyaiaabshacaqGLbGaaeyxam
% aalaaabaGaeqiUdehabaGaaGOmaiabec8aWbaacaGGBbGaaeOzaiaa
% bkhacaqGHbGaae4yaiaabshacaqGPbGaae4Baiaab6gacaqGGaGaae
% 4BaiaabkhacaqGGaGaaeyBaiaabwhacaqGSbGaaeiDaiaabMgacaqG
% WbGaaeiBaiaabwgacaqGGaGaae4BaiaabAgacaqGGaGaaeyEaiaabw
% gacaqGHbGaaeOCaiaabccacaqGLbGaaeiBaiaabggacaqGWbGaae4C
% aiaabwgacaqGKbGaaeyxaaaaaaa!94C4!
$
Would this adaptation work, is this the right way to do it?
trigonometry exponential-function
asked Dec 26 at 8:46
Sierra
244
add a comment |
I am trying to represent with spirals the growth of a capital as the Bank pays interest.
The analogy would be that the capital is represented by the radius and the passage of time by the motion of the circle with constant angular speed.
The Archimedes spiral (where radius is growing in arithmetic progression) would be the equivalent of simple interest and the logarithmic spiral would represent compound interest.
Going quantitative, I have doubts. I have tried to adapt the formulas as follows (I am stipulating that one turn is 1 year):
SIMPLE INTEREST (Archimides spiral):
$r(theta ) = atheta
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaeqiUdeha
% aa!3DBF!
$
would become
$r(theta )[{rm{final capital}}] = {rm{initial capital + a[yearly interest]}}frac{theta }{{2pi }}{rm{[fraction or multiple of year elapsed]}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaGGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaac2facqGH9aqpcaqGPbGaaeOBaiaabMgacaqG
% 0bGaaeyAaiaabggacaqGSbGaaeiiaiaabogacaqGHbGaaeiCaiaabM
% gacaqG0bGaaeyyaiaabYgacaqGRaGaaeyyaiaabUfacaqG5bGaaeyz
% aiaabggacaqGYbGaaeiBaiaabMhacaqGGaGaaeyAaiaab6gacaqG0b
% GaaeyzaiaabkhacaqGLbGaae4CaiaabshacaqGDbWaaSaaaeaacqaH
% 4oqCaeaacaaIYaGaeqiWdahaaiaabUfacaqGMbGaaeOCaiaabggaca
% qGJbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaqGVbGaaeOCaiaa
% bccacaqGTbGaaeyDaiaabYgacaqG0bGaaeyAaiaabchacaqGSbGaae
% yzaiaabccacaqGVbGaaeOzaiaabccacaqG5bGaaeyzaiaabggacaqG
% YbGaaeiiaiaabwgacaqGSbGaaeyyaiaabchacaqGZbGaaeyzaiaabs
% gacaqGDbaaaa!8D58!
$
COMPOUND INTEREST (Logarithmic spiral):
$r(theta ) = a{e^{theta b}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaamyzamaa
% CaaaleqabaGaeqiUdeNaamOyaaaaaaa!3FBD!
$
would become
$r(theta ){rm{[final capital]}} = a[{rm{initial capital]}}{e^{b[{rm{yearly interest rate]}}frac{theta }{{2pi }}[{rm{fraction or multiple of year elapsed]}}}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaqGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaab2facqGH9aqpcaWGHbGaai4waiaabMgacaqG
% UbGaaeyAaiaabshacaqGPbGaaeyyaiaabYgacaqGGaGaae4yaiaabg
% gacaqGWbGaaeyAaiaabshacaqGHbGaaeiBaiaab2facaWGLbWaaWba
% aSqabeaacaWGIbGaai4waiaabMhacaqGLbGaaeyyaiaabkhacaqGSb
% GaaeyEaiaabccacaqGPbGaaeOBaiaabshacaqGLbGaaeOCaiaabwga
% caqGZbGaaeiDaiaabccacaqGYbGaaeyyaiaabshacaqGLbGaaeyxam
% aalaaabaGaeqiUdehabaGaaGOmaiabec8aWbaacaGGBbGaaeOzaiaa
% bkhacaqGHbGaae4yaiaabshacaqGPbGaae4Baiaab6gacaqGGaGaae
% 4BaiaabkhacaqGGaGaaeyBaiaabwhacaqGSbGaaeiDaiaabMgacaqG
% WbGaaeiBaiaabwgacaqGGaGaae4BaiaabAgacaqGGaGaaeyEaiaabw
% gacaqGHbGaaeOCaiaabccacaqGLbGaaeiBaiaabggacaqGWbGaae4C
% aiaabwgacaqGKbGaaeyxaaaaaaa!94C4!
$
Would this adaptation work, is this the right way to do it?
trigonometry exponential-function
asked Dec 26 at 8:46
Sierra
244
You can represent pretty much anything with anything. Whether it will do any good is another question.
– Ivan Neretin
Dec 26 at 12:07
No doubt! I agree with both things!The fact is that it looked to me didactic, at least it guides me into the intricacies of spirals through a familiar route. But the question is whether the adaptation that I did is correct. BTW that is also a good mental exercise, but sincerely I don’t if I did it well.
– Sierra
Dec 26 at 12:14
add a comment |
I am trying to represent with spirals the growth of a capital as the Bank pays interest.
The analogy would be that the capital is represented by the radius and the passage of time by the motion of the circle with constant angular speed.
The Archimedes spiral (where radius is growing in arithmetic progression) would be the equivalent of simple interest and the logarithmic spiral would represent compound interest.
Going quantitative, I have doubts. I have tried to adapt the formulas as follows (I am stipulating that one turn is 1 year):
SIMPLE INTEREST (Archimides spiral):
$r(theta ) = atheta
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaeqiUdeha
% aa!3DBF!
$
would become
$r(theta )[{rm{final capital}}] = {rm{initial capital + a[yearly interest]}}frac{theta }{{2pi }}{rm{[fraction or multiple of year elapsed]}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaGGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaac2facqGH9aqpcaqGPbGaaeOBaiaabMgacaqG
% 0bGaaeyAaiaabggacaqGSbGaaeiiaiaabogacaqGHbGaaeiCaiaabM
% gacaqG0bGaaeyyaiaabYgacaqGRaGaaeyyaiaabUfacaqG5bGaaeyz
% aiaabggacaqGYbGaaeiBaiaabMhacaqGGaGaaeyAaiaab6gacaqG0b
% GaaeyzaiaabkhacaqGLbGaae4CaiaabshacaqGDbWaaSaaaeaacqaH
% 4oqCaeaacaaIYaGaeqiWdahaaiaabUfacaqGMbGaaeOCaiaabggaca
% qGJbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaqGVbGaaeOCaiaa
% bccacaqGTbGaaeyDaiaabYgacaqG0bGaaeyAaiaabchacaqGSbGaae
% yzaiaabccacaqGVbGaaeOzaiaabccacaqG5bGaaeyzaiaabggacaqG
% YbGaaeiiaiaabwgacaqGSbGaaeyyaiaabchacaqGZbGaaeyzaiaabs
% gacaqGDbaaaa!8D58!
$
COMPOUND INTEREST (Logarithmic spiral):
$r(theta ) = a{e^{theta b}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaamyzamaa
% CaaaleqabaGaeqiUdeNaamOyaaaaaaa!3FBD!
$
would become
$r(theta ){rm{[final capital]}} = a[{rm{initial capital]}}{e^{b[{rm{yearly interest rate]}}frac{theta }{{2pi }}[{rm{fraction or multiple of year elapsed]}}}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaqGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaab2facqGH9aqpcaWGHbGaai4waiaabMgacaqG
% UbGaaeyAaiaabshacaqGPbGaaeyyaiaabYgacaqGGaGaae4yaiaabg
% gacaqGWbGaaeyAaiaabshacaqGHbGaaeiBaiaab2facaWGLbWaaWba
% aSqabeaacaWGIbGaai4waiaabMhacaqGLbGaaeyyaiaabkhacaqGSb
% GaaeyEaiaabccacaqGPbGaaeOBaiaabshacaqGLbGaaeOCaiaabwga
% caqGZbGaaeiDaiaabccacaqGYbGaaeyyaiaabshacaqGLbGaaeyxam
% aalaaabaGaeqiUdehabaGaaGOmaiabec8aWbaacaGGBbGaaeOzaiaa
% bkhacaqGHbGaae4yaiaabshacaqGPbGaae4Baiaab6gacaqGGaGaae
% 4BaiaabkhacaqGGaGaaeyBaiaabwhacaqGSbGaaeiDaiaabMgacaqG
% WbGaaeiBaiaabwgacaqGGaGaae4BaiaabAgacaqGGaGaaeyEaiaabw
% gacaqGHbGaaeOCaiaabccacaqGLbGaaeiBaiaabggacaqGWbGaae4C
% aiaabwgacaqGKbGaaeyxaaaaaaa!94C4!
$
Would this adaptation work, is this the right way to do it?
trigonometry exponential-function
asked Dec 26 at 8:46
Sierra
244
I am trying to represent with spirals the growth of a capital as the Bank pays interest.
The analogy would be that the capital is represented by the radius and the passage of time by the motion of the circle with constant angular speed.
The Archimedes spiral (where radius is growing in arithmetic progression) would be the equivalent of simple interest and the logarithmic spiral would represent compound interest.
Going quantitative, I have doubts. I have tried to adapt the formulas as follows (I am stipulating that one turn is 1 year):
SIMPLE INTEREST (Archimides spiral):
$r(theta ) = atheta
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaeqiUdeha
% aa!3DBF!
$
would become
$r(theta )[{rm{final capital}}] = {rm{initial capital + a[yearly interest]}}frac{theta }{{2pi }}{rm{[fraction or multiple of year elapsed]}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacaGGBbGaaeOzaiaabMgacaqG
% UbGaaeyyaiaabYgacaqGGaGaae4yaiaabggacaqGWbGaaeyAaiaabs
% hacaqGHbGaaeiBaiaac2facqGH9aqpcaqGPbGaaeOBaiaabMgacaqG
% 0bGaaeyAaiaabggacaqGSbGaaeiiaiaabogacaqGHbGaaeiCaiaabM
% gacaqG0bGaaeyyaiaabYgacaqGRaGaaeyyaiaabUfacaqG5bGaaeyz
% aiaabggacaqGYbGaaeiBaiaabMhacaqGGaGaaeyAaiaab6gacaqG0b
% GaaeyzaiaabkhacaqGLbGaae4CaiaabshacaqGDbWaaSaaaeaacqaH
% 4oqCaeaacaaIYaGaeqiWdahaaiaabUfacaqGMbGaaeOCaiaabggaca
% qGJbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaqGVbGaaeOCaiaa
% bccacaqGTbGaaeyDaiaabYgacaqG0bGaaeyAaiaabchacaqGSbGaae
% yzaiaabccacaqGVbGaaeOzaiaabccacaqG5bGaaeyzaiaabggacaqG
% YbGaaeiiaiaabwgacaqGSbGaaeyyaiaabchacaqGZbGaaeyzaiaabs
% gacaqGDbaaaa!8D58!
$
COMPOUND INTEREST (Logarithmic spiral):
$r(theta ) = a{e^{theta b}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8
% qacaWGYbGaaiikaiabeI7aXjaacMcacqGH9aqpcaWGHbGaamyzamaa
% CaaaleqabaGaeqiUdeNaamOyaaaaaaa!3FBD!
$
would become
$r(theta ){rm{[final capital]}} = a[{rm{initial capital]}}{e^{b[{rm{yearly interest rate]}}frac{theta }{{2pi }}[{rm{fraction or multiple of year elapsed]}}}}
% MathType!MTEF!2!1!+-
% feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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$
Would this adaptation work, is this the right way to do it?
trigonometry exponential-function
trigonometry exponential-function
asked Dec 26 at 8:46
Sierra
244
asked Dec 26 at 8:46
Sierra
244
edited Dec 26 at 17:05
asked Dec 26 at 8:46
Sierra
244
asked Dec 26 at 8:46
Sierra
244
asked Dec 26 at 8:46
Sierra
244
244
You can represent pretty much anything with anything. Whether it will do any good is another question.
– Ivan Neretin
Dec 26 at 12:07
No doubt! I agree with both things!The fact is that it looked to me didactic, at least it guides me into the intricacies of spirals through a familiar route. But the question is whether the adaptation that I did is correct. BTW that is also a good mental exercise, but sincerely I don’t if I did it well.
– Sierra
Dec 26 at 12:14
add a comment |
You can represent pretty much anything with anything. Whether it will do any good is another question.
– Ivan Neretin
Dec 26 at 12:07
No doubt! I agree with both things!The fact is that it looked to me didactic, at least it guides me into the intricacies of spirals through a familiar route. But the question is whether the adaptation that I did is correct. BTW that is also a good mental exercise, but sincerely I don’t if I did it well.
– Sierra
Dec 26 at 12:14
You can represent pretty much anything with anything. Whether it will do any good is another question.
– Ivan Neretin
Dec 26 at 12:07
You can represent pretty much anything with anything. Whether it will do any good is another question.
– Ivan Neretin
Dec 26 at 12:07
No doubt! I agree with both things!The fact is that it looked to me didactic, at least it guides me into the intricacies of spirals through a familiar route. But the question is whether the adaptation that I did is correct. BTW that is also a good mental exercise, but sincerely I don’t if I did it well.
– Sierra
Dec 26 at 12:14
No doubt! I agree with both things!The fact is that it looked to me didactic, at least it guides me into the intricacies of spirals through a familiar route. But the question is whether the adaptation that I did is correct. BTW that is also a good mental exercise, but sincerely I don’t if I did it well.
– Sierra
Dec 26 at 12:14
add a comment |
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You can represent pretty much anything with anything. Whether it will do any good is another question.
– Ivan Neretin
Dec 26 at 12:07
No doubt! I agree with both things!The fact is that it looked to me didactic, at least it guides me into the intricacies of spirals through a familiar route. But the question is whether the adaptation that I did is correct. BTW that is also a good mental exercise, but sincerely I don’t if I did it well.
– Sierra
Dec 26 at 12:14