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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 equation \( v(t) = 700(0.76)^t \) describes the value of the cell phone over time, where \( v \) represents the value after \( t \) years. Since the initial value starts at $700 and decreases by 24% each year, the factor \( 0.76 \) represents the remaining value after depreciation.

In the context of the graph described, we can interpret the behavior of the function as follows:

• As \( t \) (the number of years since release) increases, the value \( v(t) \) decreases because the function has a decreasing exponential form.
• Initially, the value decreases at a faster rate, but as time goes on, the amount of decrease becomes smaller, leading to a slower decrease over time.

Therefore, the true statement is:

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