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) Responses $2,699.72 $2,699.72 $3,374.65 $3,374.65 $15,769.07 $15,769.07 $13,272.96

Answer 1

To calculate the future value of an investment using the continuous growth function \( A(t) = Pe^{rt} \), we need to define the variables:

• \( P = 2500 \) (the initial investment)
• \( r = 0.05 \) (the annual growth rate, expressed as a decimal)
• \( t = 6 \) (the number of years)

Now, we can plug these values into the formula:

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

Calculating the exponent:

\[ 0.05 \cdot 6 = 0.30 \]

Now we calculate \( e^{0.30} \):

Using a calculator, \( e^{0.30} \approx 1.34986 \).

Next, multiply this by the initial investment:

\[ A(6) = 2500 \cdot 1.34986 \approx 3,374.65 \]

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

Thus, the correct answer is $3,374.65.