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

Answer 1

The exponential decay model given by the equation \( v(t) = 700(0.76)^t \) suggests that the value of the cell phone decreases over time.

In exponential decay, the quantity decreases quickly at first and then slows down over time. This means that in the initial years, the phone's value drops significantly, but as time passes, the value approaches zero more gradually.

Therefore, the true statement regarding the graph of the equation is:

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