Answer:
6. The equation that models Mekhi's savings account is:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money in the account after t years
P = the initial investment ($15,000 in this case)
r = the annual interest rate (3.25% or 0.0325 as a decimal)
n = the number of times interest is compounded per year (usually 12 for monthly compounding)
t = the number of years
7. To write the equation in slope-intercept form, we need to simplify it:
A = P(1 + r/n)^(nt)
A = $15,000(1 + 0.0325/12)^(12t)
A = $15,000(1.00271)^(12t)
A = $15,000(1.00271)^12 * (1.00271)^t
A = $15,000(1.34685)^(t)
This is in exponential form, so there is no y-intercept or slope.
8. y-value: A, the amount of money in the account after t years
slope: There is no slope in an exponential equation.
9. To find out how much money will be in the savings account after 30 years:
A = $15,000(1.34685)^30
A = $15,000(10.638)
A = $159,570
Therefore, if Mekhi saves $15,000 in a savings account with a 3.25% APR for 30 years, he will have $159,570 when he retires.
10. To find out how many years Mekhi would have to work to retire with $35,000:
$35,000 = $15,000(1.34685)^t
1.34685^t = 35,000/15,000
1.34685^t = 2.3333
t = log(2.3333) / log(1.34685)
t = 9.93
Therefore, Mekhi would need to work for approximately 9.93 years (or about 10 years) to retire with $35,000, assuming he does not make any other contributions to his savings account.