Exponential Functions — Question 9

Question 9

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

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

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

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

Round all answers to two decimal places.

Question 9 - Solution

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

(a)

$$A(6)=3000e^{0.27}$$

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

(b)

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

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

(c)

$$A(8)-A(4)=3000(e^{0.36}-e^{0.18})$$

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