Jolene wants to use the next 10 years to invest for retirement, so she goes to the bank and they give her two options. The first option can be modeled by the equation y=32,000e0.05x, while the second option is modeled by the table below. Compare the two function models to decide which option Jolene should choose if she wants to invest as little money as possible up front.
Years, x 0,5,10
Money in account, y(in $) 30,000.00, 49,461.64, 81,548.45
To compare the two options, we need to calculate the amount of money Jolene would have in each account after 10 years.
For the first option:
y = 32,000e^(0.05x)
y = 32,000e^(0.05*10)
y = 32,000e^0.5
y ≈ 32,000 * 1.6487
y ≈ 52,758.40
For the second option:
After 10 years, Jolene would have $81,548.45 in the account.
Comparing the two values, Jolene would have more money in the second account after 10 years. Therefore, if she wants to invest as little money as possible up front and maximize her returns, she should choose the second option.