Part A: The growth of the investment is modeled by an exponential function.
Part B: The value of the investment in 10 years can be found using the formula:
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
In this case, P = $7,000, r = 0.046 (4.6%), n = 1 (compounded annually), and t = 10.
Plugging in these values, we get:
A = 7,000(1 + 0.046/1)^(1*10)
A = 7,000(1.046)^10
A ≈ $10,975.61
Therefore, the value of the investment in 10 years will be about $10,975.