Chapter 1.5, Problem 34E

To determine

To model:The population of US with data from $1900-2000$ and then estimate the in $1925$ and predict the population in the year $2010$ and $2020$ .

Explanation of Solution

The model of the population for the year $1900$ to $2000$ is shown in graph below.

  

Figure (1)

The best fitting exponential model for the data is,

  $y=82.2584{\left(1.13258\right)}^x$ ....... (1)

Substitute $25$ for $x$ in equation (1).

  $\begin{array}{c}y=82.2584{\left(1.13258\right)}^{25}\\ \approx 112\end{array}$

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

  $\begin{array}{c}y=82.2584{\left(1.13258\right)}^{110}\\ \approx 324\end{array}$

Substitute $120$ for $x$ in equation (1).

  $\begin{array}{c}y=82.2584{\left(1.13258\right)}^{120}\\ \approx 367\end{array}$

Therefore, the exponential model is $y=82.2584{\left(1.13258\right)}^x$ , the estimated population in year $1925$ is $112\text{million}$ , predicted population in $2010$ is $324\text{million}$ and in $2020$ is $367\text{million}$ .