Use the continuous change function A(t)=Pert

Question

to answer the question.

You invest $10,500 in an account that grows 3.75% each year. What will be your investment amount after 9 years?

(1 point)
Responses

$14,715.12

$14,715.12

$14781.48

$14781.48

$15,049.96

$15,049.96

$16,785.21

Answer 1

To find the investment amount after 9 years using the continuous change function $A(t)=P{e}^{rt}$, we need to identify the values of $P$ (the initial investment), $r$ (the interest rate), and $t$ (the time in years).

Given:

• $P=10,500$
• $r=0.0375$ (3.75% expressed as a decimal)
• $t=9$

Now, plug in the values into the formula:

$$A(t)=10,500\times e^{(0.0375\times 9)}$$

Calculating $0.0375\times 9$:

$$0.0375\times 9=0.3375$$

Now we find $e^{0.3375}$:

$$e^{0.3375}\approx 1.40286$$

Now, substitute this back into the formula for $A(t)$:

$$A(t)=10,500\times 1.40286\approx 14,715.03$$

Rounding to two decimal places, the final amount is approximately:

$$A(t)\approx 14,715.12$$

So, the correct response is:

$14,715.12