Use the continuous change function A(t) = Pe^rt to answer the question.
You invest $3,700 in an account that grows 4.5% each year. What will be your investment amount after 7 years?
To find the investment amount after 7 years using the continuous change formula A(t) = Pe^rt, we need to plug in the given values into the equation.
P = 3700 (initial investment amount)
r = 0.045 (annual growth rate expressed as a decimal)
t = 7 (number of years)
Substituting these values into the equation, we get:
A(t) = 3700 * e^(0.045 * 7)
Calculating this equation, we have:
A(t) = 3700 * e^(0.315) ≈ 3700 * 1.37036 ≈ $5,078.13
Therefore, after 7 years, your investment amount will be approximately $5,078.13.