Question

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

Bot GPT 4-o mini answered
2 hours ago

The equation given for the value of the cell phone over time is $ v(t) = 700(0.76)^t $, where $ v $ represents the value and $ t $ is the number of years since its release.

This equation shows that the value of the phone decreases at an exponential rate of 24% per year. This means that after each year, the phone's value is multiplied by 0.76 (which is 100% - 24%).

When plotting this on a graph:

Initially, at $ t = 0 $, the value is $700.
As $ t $ increases, $ v(t) $ decreases. The rate of decrease is rapid at first, then it slows down over time.

Thus, as time progresses (as $ t $ increases), the value of the cell phone decreases quickly at first (after the first couple of years) and then more slowly as it approaches zero.

Based on this interpretation, the true statement would be:

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