A lump sum of $1000 is invested at 4.4% compounded continuously. (a) Write the f

Question

A lump sum of $1000 is invested at 4.4% compounded continuously.

(a) Write the function for the model that gives the future value of the investment in dollars after t years.
F(t) = __________dollars

(b) Write a model for the rate of change of the value of the investment. (Hint: Let b = e0.044 and use the rule for f(x) = bx.)

F'(t) = ________ dollars per year

(c) How much is the investment worth after 10 years? (Round your answer to two decimal places.)
_________$

(d) How quickly is the investment growing after 10 years? (Round your answer to three decimal places.)
_________$ per year

Explanation / Answer

F(t)=F0ert

a. F(t)=1000e0.044t

b. F'(t) =1000(0.044)e0.044t = 44e0.044t

c. F(10)=1000e0.044(10)=$1552.71

d. F'(10)=44e0.044(10)=68.319

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