Chapter 6.3, Problem 60E

To determine

To Write and Explain: An exponential function $y=a{b}^x$ and the meaning of constants a and b in the real life context.

Answer to Problem 60E

Real-life population function is $y=200{(1.05)}^x$ where ‘a’ is initial population which is 200 and ‘b’ is growth factor which is 1.05.

Explanation of Solution

Given information: The exponential equation $y=a{b}^x$ .

Take an example function for the real life problem, let the initial population of a city Mexico in 2000 is 200 millions. It grows 5% each year.

So, set up equation for this as $y=200{(1+0.05)}^x$

Simplify it, which gives $y=200{(1.05)}^x$ .

The meaning for constant ‘a’ is the initial population of the Mexico.

The meaning of ‘b’ is the growth factor of the population for x number of years.