Chapter 4, Problem 27T

Solution

To find: The function that gives the number of households.

  $H\left(t\right)=62{\left(1.0485\right)}^t$

Given:

The number of households that purchased lawn and garden products is increased by about 4.85% per year from 1996 to 2001.

In 1996, about 62 million households purchased lawn and garden products.

Calculation:

Let $H$ be the number of households that purchased lawn and garden products $t$ years after 1996.

Here, the initial value is, $a=62$ , and the rate of growth is,

  $\begin{array}{c}r=\frac{4.85}{100}\\ =0.0485\end{array}$

So, the function is

  $\begin{array}{l}H\left(t\right)=a{\left(1+r\right)}^t\\ H\left(t\right)=62{\left(1+0.0485\right)}^t\\ H\left(t\right)=62{\left(1.0485\right)}^t\end{array}$