Question

Use the continuous change function A (t) = Pert to answer the question.

You invest $2,500 in an account that grows 5% each year What will be your investment amount after 6 years?

(1 point)

Ο $2,699.72

$3,374.65

$15,769.07

$13,272.96

Answer 1

To use the continuous growth function \( A(t) = Pe^{rt} \), where:

- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

Given:
- \( P = 2500 \)
- \( r = 0.05 \) (5% expressed as a decimal)
- \( t = 6 \)

Now, plug these values into the formula:

\[
A(6) = 2500 \cdot e^{0.05 \cdot 6}
\]

Calculating \( 0.05 \cdot 6 = 0.30 \):

So, we need to find \( e^{0.30} \):

Using a calculator (or an approximation),

\[
e^{0.30} \approx 1.34986
\]

Now plug this back into the formula:

\[
A(6) = 2500 \cdot 1.34986 \approx 3374.65
\]

Thus, the investment amount after 6 years will be approximately **$3,374.65**.

The answer is **$3,374.65**.