Use the image to answer the question.

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

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 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.

Answer 1

The equation \( v(t) = 700(0.76)^t \) represents the value of a cell phone over time, where \( v \) is the value and \( t \) is the number of years since its release. This equation shows an exponential decay, which means the value of the cell phone decreases over time.

With exponential decay, the value decreases quickly initially (right after the release), and as time goes on (as \( t \) increases), the amount by which the value decreases gets smaller and smaller—hence it decreases more slowly.

Therefore, the true statement is:

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