Question

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

answers below:

$2,699.72

$3,374.65

$15,769.07

$13,272.96

Answer 1

To calculate the investment amount after 6 years using the continuous change function \( A(t) = Pe^{rt} \), we need to identify the variables:

- \( P \) = initial investment = $2,500
- \( r \) = growth rate = 5% = 0.05
- \( t \) = time in years = 6

We can now plug these values into the formula:

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

Calculating the exponent:

\[
0.05 \cdot 6 = 0.3
\]

Now calculating \( e^{0.3} \) (approximately):

\[
e^{0.3} \approx 1.34986
\]

Now we can calculate \( A(t) \):

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

Rounding to two decimal places, the total amount after 6 years would be approximately **$3,374.65**.

Therefore, the correct answer is **$3,374.65**.