Question

The y-axis is labeled value left parenthesis dollars right parenthesis and ranges from 0 to 700 in increments of 100. The x-axis is labeled time left parenthesis years right parenthesis and ranges from 0 to 14 in increments of 2. The curve passes approximately through the points left parenthesis 2 comma 400 right parenthesis, left parenthesis 4 comma 230 right parenthesis, left parenthesis 6 comma 130 right parenthesis, left parenthesis 8 comma 80 right parenthesis, left parenthesis 10 comma 45 right parenthesis, left parenthesis 12 comma 25 right parenthesis, and left parenthesis 14 comma 15 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 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.
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.

Answer 1

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

Reason: v(t)=700(0.76)^t is exponential decay (factor 0.76 < 1). The value drops a large amount in the first year (700 → 532) and subsequent decreases are progressively smaller, so the graph falls steeply at first and then levels off.