Multiple Choice Average Rate Question

Question

George invests a total of $5000 into various funds on the day his daughter is born. George’s investment balance can be estimated by the function f(t)=5000 log_100(t+107)−75, where t is time in years since the investment was made. George checks on the investment every 5 years until his daughter turns 20, at which point he presents the investment to his daughter. 

Part A: During which time period did the account have the largest average rate of change? Assume t=0 on the day his daughter is born.

Part B: Interpret your result in Part A. Did George make good investments? 

Select one answer for Part A, and select one answer that is completely correct for Part B.

A:  [0,5]

B: George made bad investment decisions. He lost money over time.

B: George made excellent investment decisions. The investment balance grew more and more rapidly over time.

B: George made moderately successful investment decisions. The investment balance grew over time, but at an increasingly slow rate.

A: [15,20]

B: George made disappointing investment decisions. He did not make any money because the investment balance remained the same over each time period.

A: [5,10]

A: [10,15]

Answer 1

Hint: You will have to compare the slopes of four different secant lines to answer Part A. Looking at the slopes of all four of these secant lines will help you answer Part B.