Question

1. melanie wants to print photos for her scrapbook. the photo finishing store charges customers a rate of $0.29 per photo and a one - time fee of $5.00.

a. write a function rule for the situation:

b. find f(26):

c. interpret the meaning of f(26) in the situation:

d. does f(-18) make sense in the context of this situation? explain.

Explanation:

Step1: Write the function rule

Let \(x\) be the number of photos. The cost function \(f(x)\) has a fixed cost of \(5\) and a variable cost of \(0.29x\). So, \(f(x)=0.29x + 5\).

Step2: Calculate \(f(26)\)

Substitute \(x = 26\) into \(f(x)\):
\(f(26)=0.29\times26+5\)
First, calculate \(0.29\times26\):
\(0.29\times26=(0.3 - 0.01)\times26=0.3\times26-0.01\times26 = 7.8-0.26=7.54\)
Then, \(f(26)=7.54 + 5=12.54\)

Step3: Interpret \(f(26)\)

In the context of the problem, \(x = 26\) represents the number of photos. \(f(26)\) represents the total cost. So, it means that when Melanie prints \(26\) photos, the total cost is \(\$12.54\).

Step4: Analyze \(f(- 18)\)

Since \(x\) represents the number of photos, and the number of photos cannot be negative (\(x\geq0\) in a real - world context). So, \(f(-18)\) does not make sense because you cannot print \(-18\) photos.

Answer:

a. \(f(x)=0.29x + 5\)
b. \(12.54\)
c. When Melanie prints \(26\) photos, the total cost is \(\$12.54\)
d. No, because the number of photos \(x\) (input of the function) cannot be negative in this real - world photo - printing situation.