Question

construct an explicit rule in function notation for the arithmetic sequence represented in the graph. then determine the value of the given term and explain what it means. the graph shows total cost of a whitewater rafting trip and the corresponding number of passengers on the trip. find f(10) and explain what it represents.

Explanation:

Step1: Find the slope (common - difference)

The points are \((1,80)\), \((2,110)\), \((3,140)\), \((4,170)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((1,80)\) and \((2,110)\), \(m=\frac{110 - 80}{2 - 1}=30\).

Step2: Find the y - intercept

The equation of a line in slope - intercept form is \(y=mx + b\). Substitute \(m = 30\) and the point \((1,80)\) into \(y=mx + b\): \(80=30\times1 + b\), so \(b = 50\).

Step3: Write the function rule

The function rule in function notation for the arithmetic sequence is \(f(n)=30n + 50\), where \(n\) is the number of passengers and \(f(n)\) is the total cost.

Step4: Find \(f(10)\)

Substitute \(n = 10\) into \(f(n)=30n + 50\): \(f(10)=30\times10+50=300 + 50=350\).

Answer:

The value of \(f(10)\) is 350. It represents the total cost of the white - water rafting trip when there are 10 passengers.