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

Answer 1

The equation given for the value of a cell phone \( v(t) = 700(0.76)^t \) represents an exponential decay, where the initial value is $700 and it decreases by 24% each year (since \( 1 - 0.24 = 0.76 \)).

To interpret the graph of this equation, we note how the value behaves over time:

1. Exponential Decay: The value decreases quickly at first when \( t \) is small and then slows down as \( t \) increases. This is characteristic of exponential decay functions, where the rate of decrease diminishes over time.

Based on this analysis, the true statement is:

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