Use the continuous change function to A (t) = Pe^rt 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?
$4,795.91
$4,895.58
$5,069.96
$5,250.55
To find the investment amount after 7 years, we need to use the continuous change function A(t) = Pe^rt, where:
A(t) = the investment amount after time t
P = the initial investment amount
r = the growth rate (expressed as a decimal)
t = the number of years the investment is held
In this case, the initial investment amount P is $3,700, the growth rate r is 0.045 (4.5% expressed as a decimal), and t is 7 years.
Plugging in these values into the continuous change function:
A(t) = 3700 * e^(0.045 * 7)
Calculating this expression:
A(t) ≈ 3700 * e^(0.315)
Using a calculator or math software, we find:
A(t) ≈ 3700 * 1.370576069
A(t) ≈ 5,072.486993
Therefore, the investment amount after 7 years is approximately $5,072.49.
The closest option is $5,069.96, so the answer is $5,069.96.