Question

Which of the following are examples of exponential decay?

A: The population of a Florida is increasing by 43% every year.

B: The pesticide DDT has a half-life of 15 years.

C: March Madness has 64 teams in the bracket. Each round, half the teams are eliminated.

D: After an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours.

E: A tree frog population doubles every three weeks.

Answer 1

• B: The pesticide DDT has a half-life of 15 years.
• C: March Madness has 64 teams in the bracket. Each round, half the teams are eliminated.
• D: After an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours.

Explanation:

Exponential decay describes a situation in which the dependent variable is reduced by the same factor when the independent variable is increased by the same amount.

A — the population is increasing, not being reduced

B — the amount is cut in half when time increases by 15 years (exp. decay)

C — the number of teams is cut in half when the number of rounds increases by 1 (exp. decay)

D — the amount is cut in half when time increases by 3 hours (exp. decay)

E — the population is increasing, not being reduced