1. After dropping a ball on the floor the height of the ball will decrease after each bounce. If the equation for a ball's height is h = 10(0.75)^b where b is the number of bounces and h is the height of the ball in feet. Which graph best represents this situation?

A. Incorrect. The number of bounces (x-variable) cannot be a negative number.

B. Correct! This is an exponential decay problem. The 10 comes from the height of the ball when it was first dropped, 0.75 means the ball bounces back up 75% as high as the previous bounce or 25% less than the previous bounce.

C. Incorrect. The number of bounces (x-variable) cannot be a negative number.

D. Incorrect. This graph is increasing, an exponential growth graph, the height of the bounces decreases, or an exponential decay graph, as the number of ball bounces increases.

2. A biologist noticed that a bacteria sample doubled every day. If the initial sample contained 25 bacteria, which graph best represents this situation?

A. Correct! The graph matches the table. The equation is y = 25(2)^x because you're starting with 25 bacteria and they are doubling each day.

B. Incorrect. The bacteria are increasing, exponential growth, instead of decreasing, exponential decay.

C. Incorrect. The bacteria are increasing, exponential growth, instead of decreasing, exponential decay.

D. Incorrect. The graph shows exponential growth but the initial bacteria sample was 25 bacteria, (0, 25).

3. Mrs. Bigby invested money into an account promising the money's value would double every 12 years. If she invested $5,000 on the day of her son's birth, which graph shows how much the investment will be worth on her son's 72nd birthday?

A. Incorrect. This graph is an exponential growth graph but the initial investment is $5000 instead of $0.

B. Incorrect. The graph is an exponential growth graph but the investment doubles every 12 years.

C. Correct! The equation of the curve is y = 5000(2)x/12 because the initial investment is $5,000 and the money doubled every 12 years.

D. Incorrect. The graph is an exponential growth graph but the investment doubles every 12 years.

4. The metastable form of Technetium-99 (Tc-99m) is used in nuclear medicine procedures. It decays, losing half its mass every hour. If a doctor checks on a patient six hours after the isotope has been administered and 10 micrograms of it still remain, which graph will determine the correct amount of Tc-99m administered to the patient?

A. Correct! The equation is y = 640 1/2^x, the doctor initially gave the patient 640 micrograms and the medicine was halved each hour.

B. Incorrect. This is an exponential decay graph except the medicine is being divided in half every hour.

C. Incorrect. This is an exponential decay graph except the medicine is being divided in half every hour.

D. Incorrect. This is an exponential decay graph except the medicine is being divided in half every hour.