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?
A. $4,795.91
B. $4,895.58
C. $5,069.96
D. $5,250.55
The continuous change function is given as A(t) = Pe^rt, where:
A(t) is the investment amount at time t,
P is the initial investment amount,
r is the annual interest rate expressed as a decimal, and
t is the time in years.
In this case, P = $3,700, r = 0.045 (4.5% expressed as a decimal), and t = 7 years.
Using the formula, we can calculate the investment amount after 7 years:
A(7) = 3700 * e^(0.045 * 7)
Calculating the exponential term:
e^(0.045 * 7) ≈ 1.33444897
Calculating the investment amount:
A(7) ≈ 3700 * 1.33444897 ≈ 4933.92
Rounding to the nearest cent, the investment amount after 7 years is approximately $4,933.92.
Among the given answer choices, the closest amount to $4,933.92 is $4,895.58.
Therefore, the correct answer is B. $4,895.58.