Question

directions: the function $v(t)=250,000(1.038)^t$ represents the value (v) of a home t years after its initial purchase. interpret the annual percent rate of change in this context. workspace: solution: name:____ period____ ma.912.ar.5

Explanation:

Step1: Identify the general form of exponential - growth function

The general form of an exponential - growth function is $V(t)=V_0(1 + r)^t$, where $V_0$ is the initial value, $r$ is the annual percent rate of change (as a decimal), and $t$ is the number of years.

Step2: Compare the given function with the general form

The given function is $V(t)=250000(1.038)^t$. Comparing it with $V(t)=V_0(1 + r)^t$, we can see that $1 + r=1.038$.

Step3: Solve for $r$

Subtract 1 from both sides of the equation $1 + r=1.038$. So, $r=1.038−1 = 0.038$.

Step4: Convert $r$ to a percentage

To convert $r$ from a decimal to a percentage, multiply by 100. So, $r = 0.038\times100=3.8\%$.

Answer:

The annual percent rate of change is $3.8\%$. This means that the value of the home increases by $3.8\%$ each year after its initial purchase.