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

Question

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

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 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.

Answer 1

Bot GPT 4-o mini answered
3 hours ago

The situation you described involves the exponential depreciation of a cell phone's value. The value $ v(t) = 700(0.76)^t $ shows that the value decreases over time, as the factor of $ 0.76 $ is less than 1 (indicating a 24% decrease per year).

To interpret the graph of this equation:

At $ t = 0 $, the value is $700.
As $ t $ increases, $ v(t) $ becomes a smaller number since each year, the phone retains only 76% of its value from the previous year.

In an exponential decay model like this, the value decreases quickly at first but then slows down as time goes on, because each year the amount subtracted (or lost) is proportional to the current value.

Thus, the correct statement to identify is:

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