Chapter 6.1, Problem 21E

a

To determine

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

Answer to Problem 21E

The model represent exponential decay

Explanation of Solution

Given information:

The value of mountain bike $y$ (in dollar) can be approximated by the model $y=2500{\left(0.75\right)}^t$ ,where $t$ is the number of year.

the base 0.75 is greater than 0 and less than 1,so the model represents exponential decay.

Hence, model represent exponential decay.

b

To determine

To identify the annual percent increase or decrease in the value of the bike .

Answer to Problem 21E

The annual decrease in the value of bike is 25%

Explanation of Solution

Given information:

The value of mountain bike $y$ (in dollar) can be approximated by the model $y=2500{\left(0.75\right)}^t$ ,where $t$ is the number of year.

Because $t$ is given in year and decay factor is $0.75=1-0.25$ ,the annual percent decrease is 0.25 or 25%

Hence, the annual decrease in the value of bike is 25%

c

To determine

To estimate the time when the value of the bike will be $50.

Answer to Problem 21E

The time when the value of the bike will be $50 in 4.82 years

Explanation of Solution

Given information:

The value of mountain bike $y$ (in dollar) can be approximated by the model $y=2500{\left(0.75\right)}^t$ ,where $t$ is the number of year.

Use the trace feature of a graphing calculator to determine that $y=50$ when $t\approx 4.82$ . After approximate 4.82 the value of price will about $50.

  

Hence, the time when the value of the bike will be $50 in 4.82 years.