Chapter 1.5, Problem 33E

To determine

To model:The population of the world with data from $1950-2000$ and then estimate the in $1993$ and predict the population in the year $2010$ .

Explanation of Solution

The model of the population for the year $1950$ to $2000$ is shown in graph below.

  

Figure (1)

The best fitting exponential model for the data is,

  $y=534.35{\left(1.02296\right)}^x+1034.22$ ....... (1)

Substitute $93$ for $x$ in equation (1).

  $\begin{array}{c}y=534.35{\left(1.02296\right)}^{93}+1034.22\\ =5446.93\\ \approx 5447\end{array}$

Substitute $110$ for $x$ in equation (1).

  $\begin{array}{c}y=534.35{\left(1.02296\right)}^{110}+1034.22\\ =7525.15\\ \approx 7525\end{array}$

Therefore, the exponential model is $y=534.35{\left(1.02296\right)}^x+1034.22$ , the estimated population in year $1993$ is $5447$ and predicted population is $7525$ .