Answer:
The function for the balance in a savings account over time, given an initial deposit (P) and an annual interest rate (r), is:
A = P(1 + r)^t
Where A is the balance, P is the initial deposit, r is the annual interest rate (expressed as a decimal), and t is the number of years.
In this case, Vanessa has deposited $12,000, and the annual interest rate is 3.5% or 0.035 as a decimal, so the function is:
A = 12000(1 + 0.035)^t
To find out what her balance will be after 5 years, we can substitute t = 5 into the function:
A = 12000(1 + 0.035)^5
A = 12000(1.035)^5
A = 12000*1.2094
A = $14,512.8
Vanessa's balance will be $14,512.8 after 5 years.
Explanation: