Question

the average price of a movie ticket in the united states from 2001 to 2014 is modeled by the expression 4.62 + 0.28x, where x represents the number of years since 2001. a. identify the part(s) of the expression that corresponds to the cost of movie tickets in 2001. b. interpret the meaning of 0.28. daniel car rental company gives cars on rent on hourly basis. the cost of hiring is a base fee of $22 plus $.42 per mile. a. define a variable and write an expression to represent the situation. b. ashley rented a car and drove 250 miles. what is the total amount ashley paid to rent the car? solution: a. b.

Explanation:

Left Side:

A.

In the linear expression \(4.62 + 0.28x\), when \(x = 0\) (since \(x\) is the number of years since 2001, for the year 2001 \(x=0\)), the value of the expression is \(4.62\). So the part of the expression that corresponds to the cost of movie tickets in 2001 is \(4.62\).

In the linear expression \(y=mx + b\) (where \(y = 4.62+0.28x\) in this case), \(m\) is the slope. Here, \(m = 0.28\). Since \(x\) is the number of years since 2001 and \(y\) is the average price of a movie ticket, the \(0.28\) represents the rate of change of the average price of a movie ticket per year. That is, the average price of a movie ticket increases by \(0.28\) dollars per year.

Let \(m\) be the number of miles driven. The base - fee is \(22\) dollars and the cost per mile is \(0.42\) dollars. Using the formula for a linear cost function \(C=\text{fixed cost}+\text{variable cost}\), the expression for the cost \(C\) of renting a car is \(C = 22+0.42m\).

Answer:

\(4.62\)

B.