Chapter MPS, Problem 8.3MPS

a.

To determine

To find: The exponential function which can be useful in modeling US population.

Answer to Problem 8.3MPS

The exponential function which can be useful in modeling US population is $y=3.39{\left(1.03\right)}^x$ .

Explanation of Solution

Given information: The US population in 1790 was 3.39 million and in 1800 the population was 5.31 million.

Calculation:

The exponential function is,

  $\begin{array}{c}y=abx\\ =\left(3.93\right)\left(5.31\right)x\end{array}$

The equation in terms of $x$ is,

  $\begin{array}{l}y=a{b}^x\\ 5.31=3.93b^{10}\\ 1.3151=b^{10}\\ b=1.03\end{array}$

Thus, the equation is,

  $y=3.39{\left(1.03\right)}^x$

b.

To determine

To find: The population in the year 1820,1840 and 1860.

Answer to Problem 8.3MPS

The population in the year 1820,1840 and 1860 is 9.54, 17.23 and 31.12 million respectively.

Explanation of Solution

Given information: The US population in 1790 was 3.39 million and in 1800 the population was 5.31 million.

Calculation:

Consider the equation.

  $y=3.39{\left(1.03\right)}^x$

The population in 1820 is,

  $\begin{array}{c}y=3.39{\left(1.03\right)}^{30}\\ =9.54\end{array}$

The population in 1840 is,

  $\begin{array}{c}y=3.39{\left(1.03\right)}^{50}\\ =17.23\end{array}$

The population in 1860 is,

  $\begin{array}{c}y=3.39{\left(1.03\right)}^{70}\\ =31.12\end{array}$

Thus, the population in the year 1820,1840 and 1860 is 9.54, 17.23 and 31.12 million respectively.