Chapter 6.1, Problem 22E

a

To determine

To tell whether the model represent exponential growth or exponential decay.

Answer to Problem 22E

The model represent exponential growth.

Explanation of Solution

Given information:

The population $P$ (in thousand) of Austin, Texas, during a recent decade can be approximated by $y=494.29{\left(1.03\right)}^t$ ,where $t$ is the number of year.

The base 1.03 is greater than 1,so the model represents exponential growth.

Hence, model represent exponential growth.

b

To determine

To identify the annual percent increase or decrease in the population.

Answer to Problem 22E

The annual percent increase is 0.03 or 3%

Explanation of Solution

Given information:

The population $P$ (in thousand) of Austin, Texas, during a recent decade can be approximated by $y=494.29{\left(1.03\right)}^t$ ,where $t$ is the number of year.

Because $t$ is given in year and growth factor is $1.03=1+0.03$ ,the annual percent increase is 0.03 or 3%

Hence, the annual percent increase is 0.03 or 3%.

c

To determine

To estimate the time when the population was about 590000.

Answer to Problem 22E

The time when the population was about 590000 in 6 years.

Explanation of Solution

Given information:

The population $P$ (in thousand) of Austin, Texas, during a recent decade can be approximated by $y=494.29{\left(1.03\right)}^t$ ,where $t$ is the number of year.

Use the trace feature of a graphing calculator to determine that $y=590000$ when $t=6$ . After 6 year the population was about 590000

  

Hence, the time when the population was about 590000 in 6 years.