Exponential Functions — Question 9

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Question 9

A savings account earns interest compounded continuously at an annual rate of 4.5 A(t)=3000e0.045tA(t) = 3000e^{0.045t}

  • (a) How much money will be in the account after 6 years?

  • (b) How long will it take for the account to reach $5,000?

  • (c) How much interest is earned between years 4 and 8?

Round all answers to two decimal places.

Original worksheet page 1: question and worked solution for 1-7-009
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Question 9 - Solution

Use the exact exponential model and keep full precision until the final rounding.

(a)

A(6)=3000e0.27A(6)=3000e^{0.27}

3929.89dollars\boxed{3929.89\quad\text{dollars}}

(b)

t=ln⁡(5000/3000)/0.045t=\ln(5000/3000)/0.045

11.35years\boxed{11.35\quad\text{years}}

(c)

A(8)−A(4)=3000(e0.36−e0.18)A(8)-A(4)=3000(e^{0.36}-e^{0.18})

708.34dollars\boxed{708.34\quad\text{dollars}}

Original worksheet page 2: question and worked solution for 1-7-009

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