Question

Exponential Functions from Situations Quick Check
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.
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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.