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.
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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The equation given for the value of the cell phone is \( v(t) = 700(0.76)^{t} \), where \( v \) is the value of the cell phone and \( t \) is the number of years since its release date.
Since the coefficient \( 0.76 \) is less than 1, it indicates that the value \( v(t) \) decreases over time.
In an exponential decay model like this, the value decreases quickly initially and then the rate of decrease slows down as time goes on. Therefore, as \( t \) increases, \( v(t) \) decreases quickly at first, then more slowly.
Based on this interpretation, the true statement is:
**As t increases, v decreases quickly at first and then slowly.**
Since the coefficient \( 0.76 \) is less than 1, it indicates that the value \( v(t) \) decreases over time.
In an exponential decay model like this, the value decreases quickly initially and then the rate of decrease slows down as time goes on. Therefore, as \( t \) increases, \( v(t) \) decreases quickly at first, then more slowly.
Based on this interpretation, the true statement is:
**As t increases, v decreases quickly at first and then slowly.**
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