Question

Which situations are best modeled by an exponential relationship? Select all that apply.

A. A tree frog population in a national forest doubles every three weeks.

B. Every year, attendance at an amusement park increases in spring and decreases in autumn.

C. The total amount of emails if every person that receives an email forwards the email to five friends.

D. A district-wide basketball tournament eliminates 50% of the participant teams after each game.

F. A savings account earns 7.5% interest every month for the first 12 months, and then no longer earns interest.

Answer 1

An exponential relationship is best modeled when a quantity grows or decreases by a constant percentage over a fixed interval of time or distance.

Step-by-step explanation:

An exponential relationship is best modeled when a quantity grows or decreases by a constant percentage over a fixed interval of time or distance. Based on this definition, the situations that are best modeled by an exponential relationship are:

• A. A tree frog population in a national forest doubles every three weeks. The population size is growing by a constant percentage (doubling) over a fixed interval of time (three weeks).
• C. The total amount of emails if every person that receives an email forwards the email to five friends. Each person forwarding the email is increasing the total number of emails by a constant percentage (multiplying by five) over a fixed interval of time (each time the email is forwarded).
• F. A savings account earns 7.5% interest every month for the first 12 months, and then no longer earns interest. The amount of interest earned on the savings account is growing by a constant percentage (7.5%) over a fixed interval of time (each month).