Question

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

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

As t increases, v decreases quickly at first and then slowly.
As t increases, v decreases quickly at first and then slowly.
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Answer 1

The given situation describes an exponential decay model for the value of a cell phone, represented by the equation \( v(t) = 700(0.76)^t \). Since the multiplier \( 0.76 \) is less than 1, the value \( v(t) \) will decrease over time as \( t \) (the number of years since the phone was released) increases.

In an exponential decay model, the value typically decreases quickly at first and then more slowly as time goes on. Therefore, as \( t \) increases, the decline in the value of the cell phone becomes less pronounced.

From the provided response options, the true statement is:

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