Exercise 60 Page 514

We want to determine whether the given function represents exponential growth or exponential decay. Let's recall the general form of an exponential function.

Growth or Decay?

The value of $b$ tells us whether the function is growth or decay.

• If $b>1,$ the function represents exponential growth.
• If $0<b<1,$ the function represents exponential decay.

Let's consider the given function. We can see that $b=\frac{1}{2}.$ Since $b<1,$ the function represents exponential decay.

Determining the $y\text{-}$intercept

The $y\text{-}$intercept of an exponential function is $(0,a).$ Looking back at the given function, we can see that $a=3.$ Therefore, the $y\text{-}$intercept is $\left(0,3\right).$