Question

The population of a town over the past 10 years can be represented with the equationy = 2450(1.07)? What is the rate of change?A) 1.07%B 2450C 7%D.0796

Answer 1

Let's begin by identifying key information given to us:

The population is represented by the equation:

`y=2450\mleft(1.07\mright)`

We will compare the equation for the population with the general exponential growth equation, we have:

`\begin{gathered} f(x)=a(1+r)^x \\ where\colon \\ f(x)=exponential\text{ }growth\text{ }function \\ a=initial\text{ }amount \\ r=growth\text{ }rate \\ x=number\text{ }of\text{ }time\text{ }intervals \end{gathered}`

Comparing, we have:

`\begin{gathered} f(x)\Rightarrow y \\ a=2450 \\ (1+r)=1.07\Rightarrow r=1.07-1=0.07 \\ \Rightarrow r=0.07=7\text{\%} \\ \\ \\ \end{gathered}`

Therefore, the rate of change is 7%. Hence, C is the answer