The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. The independent variable is the number of people. The initial value (initial fee) for the picnic is $40. The rate of change is $8.67 per person. As the number of people increases, the total cost of the picnic increases. If 4 people attended the picnic, the total cost would be $46.
Accepted Solution
A:
Answer:The correct options are:The independent variable is the number of people. The initial value (initial fee) for the picnic is $40. As the number of people increases, the total cost of the picnic increases.Step-by-step explanation:We are given a set of value in a table form that shows the linear relationship between the number of people at a picnic and the total cost of the picnic as: Number of people Total cost($) 6 52 9 58 12 64 15 70So as the total cost depend on the number of people at the picnic.Hence, the number of people will act as a independent variable and the total cost will represent the dependent variable.Now as the table shows the linear relationship.Hence we will find out the function that represent the total cost in terms of the number of people with the help of two values.Let f(n) represents the cost of n people.As the linear function pass through (6,52) and (9,58).Hence, the function is given by:[tex]f(n)-52=\dfrac{58-52}{9-6}\times (n-6)\\\\f(n)-52=\dfrac{6}{3}\times (n-6)\\\\f(n)-52=2(n-6)\\\\f(n)-52=2n-12\\\\f(n)=2n-12+52\\\\f(n)=2n+40[/tex]Hence, the initial value for the picnic is the cost of the function f(n) when n=0Hence when n=0 we have:f(0)=40Hence, initial cost is $ 40.The rate of change is the slope of the linear function so by looking at the function we see that the rate of change is $ 2.( Since, f(n)=2n+40 )Clearly from the set of values we see that as the number of people increases the total cost of the picnic also increases.If 4 people attend the picnic i.e. n=4The cost of picnic is calculated as:f(4)=2×4+40f(4)=8+40f(4)=48Hence, total cost for 4 people is: $ 48.