Chapter 6.2, Problem 54E

To determine

Whether the function represents the exponential growth or exponential decay after rewriting it.

Answer to Problem 54E

Rewriting the function as $f(t)=0.3448{\left(1.16\right)}^t$ . It represents the exponential growth.

Explanation of Solution

Giveninformation:

The function is $f(t)=0.4{\left(1.16\right)}^{t-1}$ .

Rewriting the given function as follows:

  $\begin{array}{l}f(t)=0.4{\left(1.16\right)}^{t-1}\\ \Rightarrow f(t)=0.4\cdot \frac{{\left(1.16\right)}^t}{1.16}(\because \text{Quotient of Powers Property})\\ \Rightarrow f(t)=0.3448{\left(1.16\right)}^t\end{array}$

Now, comparing the function with $f(x)=a{b}^x$ , we can notice that $a=0.3448>0$ and $b=1.16>1$ .

Conclusion:

Therefore, the function represents the exponential growth.