The future value that accrues when $400 is invested at 4%, compounded continuously, isS(t) = 400eº0.04twhere t is the number of years.Exercise (a)At what rate is the money in this account growing when t = 7?Step 1To find the rate the money is growing, we find the rate of change of S with respect to t. That is, take thederivative of S(t). The function is a constant multiple of a natural exponential function. Therefore, we use thedychain rule for differentiating natural exponential functions:duwhere u is a differentiable function.dxeu.xpThus,S'(t):dollars per year. The rate at which the money is growing is expressed by the derivative of the function, which we found in part(a).S'(t) = 16e0.04tUse the derivative to find the rate of change evaluated at t = 13 years.0.04= 16eS'(13)

Consider the future value compounded continuously is St=400e0.04t Here, the objective is to find the…

The future value that accrues when $400 is invested at 4%, compounded continuously, is S(t) = 400e0.04t where t is the number of years. Exercise (a) At what rate is the money in this account growing when t = 7?

The future value that accrues when $400 is invested at 4%, compounded continuously, is S(t) = 400e0.04t where t is the number of years. Exercise (a) At what rate is the money in this account growing when t = 7?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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A: Solution:-

Question

The future value that accrues when $400 is invested at 4%, compounded continuously, is
S(t) = 400eº
0.04t
where t is the number of years.
Exercise (a)
At what rate is the money in this account growing when t = 7?
Step 1
To find the rate the money is growing, we find the rate of change of S with respect to t. That is, take the
derivative of S(t). The function is a constant multiple of a natural exponential function. Therefore, we use the
dy
chain rule for differentiating natural exponential functions:
du
where u is a differentiable function.
dx
eu.
xp
Thus,
S'(t):
dollars per year.

The rate at which the money is growing is expressed by the derivative of the function, which we found in part
(a).
S'(t) = 16e0.04t
Use the derivative to find the rate of change evaluated at t = 13 years.
0.04
= 16e
S'(13)

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