Mateo is saving money for college. He put $\$1000$ in a no-interest, no fees checking account. At the end of each year his grandparents give him $\$200$ to add to the account. Mateo’s friend Marcy has saved $\$1000$, and she put this money into an investment that earns $8\%$ annual interest. At the end of each year, Marcy pays an investment management fee of $\$15$ and she adds $\$100$ to the account from her babysitting earnings.

1. Make a table showing how much money Mateo and Marcy will have in their accounts at the end of each year for the first five years. Start your table with Year $0$.

   Answer (a):

   Year	Mateo $(\$)$	Marcy $(\$)$
   $0$	$1000$	$1000$
   $1$	$1200$	$1165.00$
   $2$	$1400$	$1343.20$
   $3$	$1600$	$1535.66$
   $4$	$1800$	$1743.51$
   $5$	$2000$	$1967.99$

2. What was the average rate of change of each account from Year $0$ to Year $2$? Show your work and include units in your answers.

   Hint (b):

   $\frac{\text{(money at year 2)-(money at year 0)}}{2-0}$

3. What was the average rate of change from Year $3$ to Year $5$ in each account?

   Hint (c):

   Refer to part (b).

4. Whose account will have more money in the long run? Explain using your results from part (b) and part (c).

   Hint (d):

   Does linear or exponential grow faster in the long run?