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

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.