Question

Use the continuous change function A(t) = Pe^rt 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?

A.
$14,715.12

B.
$14781.48

C.
$15,049.96

Answer 1

A

note that r = 3.75% = 0.0375

A(9) = 10500 ×
`e^(0.0375(9))` = 10500 ×
`e^(0.3375)` = 14, 715.12

Answer 2

We are given formula for continuous change function A(t) = Pe^rt.

We need to find the value of $10,500 investment amount grows 3.75% each year after 9 years.

Plugging values of P=10500

r= 3.75% = 0.0375 and

t=9 in given formula.

We get

`A(9) = 10500e^(0.0375* 9)`

Let us simplify it now.

`e^(0.0375* 9)=e^(0.3375)=1.40144`

`=10500* \:1.40144\dots`

`\mathrm{Multiply\:the\:numbers:}\:10500* \:1.40144\dots =14715.11589\dots`

Rounding it to the nearest cents.

=14715.12.

Therefore, $14715.12 will be investment amount $10,500 after 9 years.