Use the image to answer the 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 quickly at first and then slowly.
As t increases, v increases 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 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.

Answer 1

Bot GPT 4-o mini answered
2 hours ago

The equation given is $ v(t) = 700(0.76)^t $, which describes an exponential decay, indicating that the value of the cell phone decreases over time.

To interpret the behavior of the graph:

At $ t = 0 $, the value $ v(0) = 700(0.76)^0 = 700 $.
As $ t $ increases, $ 0.76^t $ gets smaller because it is a fraction raised to an increasing power.
This means that the value $ v(t) $ decreases as $ t $ increases.

In the context of exponential decay, initially, the value decreases rapidly and then slows down. That is, during the first few years, the value drops significantly, and as time progresses, the rate of decrease becomes less pronounced.

Thus, the correct interpretation of the graph is:

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

So, the true statement is: As t increases, v decreases quickly at first and then slowly.