Nathaniel purchases a one-year membership pass to an art museum. As a member, he receives a discounted entrance fee. The total cost for the year, f(x), after x visits to the art museum is shown on the graph below.

What is the discounted members entrance fee to the art museum, and what would be the total cost after 20 visits?

A. The discounted entrance fee to the art museum is $2.00. The total cost is $52.00 after 20 visits.
B. The discounted entrance fee to the art museum is $2.50. The total cost is $62.00 after 20 visits.
C. The discounted entrance fee to the art museum is $3.00. The total cost is $72.00 after 20 visits.
D. The discounted entrance fee to the art museum is $1.50. The total cost is $42.00 after 20 visits.

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gmany gmany · Answer 1 · 2018-10-06T20:30:03+02:00

It's a linear function with y-intercept = 12.

The slope-intercept form:

[tex]f(x)=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Let's read the coordinates of two points on the graph:

(2, 15) and (4, 18)

Substitute to the formula of a slope:

[tex]m=\dfrac{18-15}{4-2}=\dfrac{3}{2}=1.5[/tex]

We have the equation of a line:

[tex]\boxed{f(x)=1.5x+12}[/tex]

We need calculate the value of function for x = 1 and x = 20.

Substitute:

[tex]f(1)=1.5(1)+12=13.5[/tex]

[tex]f(20)=1.5(20)+12=30+12=42[/tex]

$12 is the "Fixed Fee", therefore the discounted entrance fee to the art museum is

[tex]\$13.50-\$12.00=\$1.50[/tex]

The total cost is $42.00 after 20 visits.