Question

choosing a graph to represent a verbal description
which graph models a function showing a piece of equipment that has an original value of $5,000 and whose value decreases by 15% each year?

Explanation:

Step1: Write the exponential - decay formula

The formula for exponential decay is $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $a = 5000$, $r=0.15$, so the function is $y = 5000(1 - 0.15)^t=5000\times0.85^t$.

Step2: Analyze the properties of the function

When $t = 0$, $y=5000\times0.85^0 = 5000$. As $t$ increases, since $0<0.85<1$, the value of $y$ will decrease. The graph of the function $y = 5000\times0.85^t$ is a decay - type exponential function. It starts at the point $(0, 5000)$ and decreases as $t$ (the number of years) increases.

Answer:

The third graph (the one that starts at $y = 5500$ (close to 5000) and decreases as $x$ (years) increases)