Which of the contexts below could be modeled by an exponential function?

Question

Answer
Multiple Choice Answers
Eva puts $50 a month into a savings account.
Snow was falling at a rate of 0.75 inches per hour.
The amount of a certain medication in a person's bloodstream decreases by one fifth
5
1
​
every week.
A smartphone data plan charges a $65/month and $0.71/GB of data used.

Answer 1

The context that could be modeled by an exponential function is:

The amount of a certain medication in a person's bloodstream decreases by one fifth (1/5) every week.

This situation describes a process of decay, where the amount of medication decreases by a constant proportion (one fifth) over regular intervals (every week), which is characteristic of an exponential decay function.

The other options describe linear relationships or constant rates, which are not modeled by exponential functions:

• Eva puts $50 a month into a savings account – This is a linear growth scenario.
• Snow was falling at a rate of 0.75 inches per hour – This also represents a constant rate, which is linear.
• A smartphone data plan charges a $65/month and $0.71/GB of data used – This describes a linear relationship based on data usage.