Question

select the correct answer from each drop - down menu.
jerry invested $300 in a bank that pays 5 percent interest compounded annually. the amount of money he has at the end of each year is modeled by the function ( j(t)=300(1.05)^{t} ). his sister rachel invested the same initial amount of money into a different bank that paid her 5.5 percent simple interest. the amount she gets at the end of each year is shown in the table.

year	amount (dollars)
1	316.50
2	333.00
3	349.50
4	366.00
5	382.50

the average rate of growth for jerry’s investment from when he first put money in the bank to the end of the third year is $ drop - down per year.
the average rate of growth for rachel’s investment from when she first put money in the bank to the end of the third year is $ drop - down per year.

Explanation:

Step1: Find Jerry's final amount at year 3

$J(3) = 300(1.05)^3 = 300 \times 1.157625 = 347.2875$

Step2: Calculate Jerry's average growth rate

$\text{Average Rate} = \frac{347.2875 - 300}{3-0} = \frac{47.2875}{3} = 15.7625$

Step3: Find Rachel's final amount at year3

Rachel's year 3 amount = $349.50$

Step4: Calculate Rachel's average growth rate

$\text{Average Rate} = \frac{349.50 - 300}{3-0} = \frac{49.50}{3} = 16.50$

Answer:

Jerry's average growth rate is $\boldsymbol{15.76}$ per year, Rachel's average growth rate is $\boldsymbol{16.50}$ per year.