Exponential Functions from Situations Quick Check

Question

4 of 54 of 5 Items

Question
Use the image to answer the question.

A decreasing curve with an arrow on the end is plotted on a coordinate plane. The curve begins at the point left parenthesis 0 comma 700 right parenthesis.

The value of a cell phone decreases exponentially at a rate of 24% each year after its release date. If the initial value of the phone is $700, the situation can be modeled by the equation v(t)=700(0.76)t , where v is the value of the cell phone t years since its release date. Interpret the graph of the equation and identify the true statement.

(1 point)
Responses

As t increases, v decreases slowly at first and then quickly.
As t increases, v decreases slowly at first and then quickly.

As t increases, v decreases quickly at first and then slowly.
As t increases, v decreases quickly at first and then slowly.

As t increases, v increases slowly at first and then quickly.
As t increases, v increases slowly at first and then quickly.

As t increases, v increases quickly at first and then slowly.
As t increases, v increases quickly at first and then slowly.
Skip to navigation

Answer 1

The graph of the equation \( v(t) = 700(0.76)^t \) represents an exponential decay function, indicating that the value of the cell phone decreases over time. Since the cell phone loses 24% of its value each year, it retains 76% of its value from the previous year.

In the context of the given options, the appropriate interpretation of the graph is:

As t increases, v decreases quickly at first and then slowly.

This statement correctly describes how the value of the cell phone drops more significantly in the earlier years and then levels off, decreasing at a slower rate over time.