Q. 4.23 - Elementary Statistics

Question

Rental-Car Costs. During one month. the Avis Rent-A-Car rate for renting a Buick LeSabre in Mobile. Alabama, was \(68.22 per day plus 25\) per mile. For a 1-day rental, let x denote the number of miles driven and let y denote the total cost, in dollars.

a. Find the equation that expresses y in terms of x.

b. Determine b₀ and b₁ .

c. Construct a table similar to Table 4.1 on page 158 for the x-values 50,100 ,and 250 miles.

d. Draw the graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line.

e. Apply the graph from part (d) to estimate visually the cost of driving the car 150 miles. Then calculate that cost exactly by using the equation from part (a).

Step-by-Step Solution

Answer

a. Equation representing $y$ in terms of $x$ is $y=25x+68.22$.

b. $b_0 =68.22$ and $b_1 = 25$

c. Table is given below.

d. Graph is given below.

e. The cost of driving the car $150$ miles is $3818.22.

Part(a) Step 1: Given information

We need to find equation which represents y in terms of x.

Part(a) Step 2: Explanation

For 1-day rental $68.22$ is constant and total cost will be $25*(miles driven)$.

$x=$miles driven

$y=$total cost

so, the equation will be $y=25x+68.22$

Part(b) Step 1: Given information

we need to find value of b₀ and b₁

Part(b) Step 2: Explanation

General form of linear equation is $y= b_0+b_{1}x$

Comparing $y=25x+68.22$ with general form we get,

b₀=$68.22$ and b₁=$25$.

Part(c) Step 1: Given information.

We need to find the table for x-values $50$,$100$ ,and $250$ miles .

Part(c) Step 2: Explanation

Table is given below

Miles x	Total cost($) y
50	1318.22
100	2568.22
250	6318.22

Part(d) Step 1: Given information

We need to plot the graph of above linear equation.

Part(d) Step 2: Explanation

Graph for above linear equation is 

Part(d) Step 1: Given information

We need to estimate the cost of driving the car $150$ miles using graph first and then calculate exact value of cost by using linear equation.

Part(d) Step 2: Explanation

According to graph the estimate value of cost for $150$ miles is around $\$3800$

if we put the value of $x=150$ we get $y=3818.22$

So the exact cost is $\$3818.22$