Chapter 6.3, Problem 24E

a.

To determine

To find:Length of vacation each resort cost the same.

Answer to Problem 24E

Length of vacation does each resort cost about the same = $9$ nights.

Explanation of Solution

Given:

The room expenses for two different resorts given.

Concept Used:

Use patterns between consecutive data pairs to determine type of function. Linear function: - The difference of consecutive y-values is constant. Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Calculation:

Linear function: - The difference of consecutive y-values is constant. Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Picture given: -

  

Length of vacation does each resort cost about the same = $9$ nights.

Hence,

Length of vacation does each resort cost about the same = $9$ nights.

b.

To determine

To find:Whether sea breeze resort more expensive than blue water resort.

Answer to Problem 24E

Yes, because the cost at Sea Breeze Resort shows exponential growth, it will eventually be greater than the cost at Blue Water Resort, which shows linear growth.

Explanation of Solution

Given:

The room expenses for two different resorts given.

Concept Used:

Use patterns between consecutive data pairs to determine type of function. Linear function: - The difference of consecutive y-values is constant. Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Calculation:

Linear function: - The difference of consecutive y-values is constant. Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Picture given: -

  

Blue water resort charges $\$1450$ for the first three nights & $\$105$ for each additional night.

Hence,

Yes, because the cost at Sea Breeze Resort shows exponential growth, it will eventually be greater than the cost at Blue Water Resort, which shows linear growth.

c.

To determine

To find:Blue water resort ever be more expensive than sea breeze resort.

Answer to Problem 24E

The total cost is always greater at Sea Breeze Resort.

Explanation of Solution

Given:

The room expenses for two different resorts given.

Concept Used:

Use patterns between consecutive data pairs to determine type of function. Linear function: - The difference of consecutive y-values is constant. Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Calculation:

Linear function: - The difference of consecutive y-values is constant. Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Picture given: -

  

Sea Breeze resort charges $\$1200$ for the first three nights & $10\%$ increase for each additional night.

No, the cost of the first three nights is greater at Sea Breeze Resort than at Blue Water Resort. Also, the cost of each additional night at Sea Breeze Resort is greater than the cost of each additional night at Blue Water Resort.

Hence,

The total cost is always greater at Sea Breeze Resort.