Comparing Functions and Initial Value

Lee charges $3 for a basket and $2.50 for each pound of fruit picked at the orchard. Write an equation for the total cost of x pounds of fruit from the orchard.

• y = 3x + 2.5

• y = 2.50x + 3

• y = 2.50x 

• y = 3x + 2.50

Write an equation for the line

• y = 50x

• y = 20x

• y = 0.02x

• y = 0.2x

What is the y-intercept?

• (0,7)

• (0, 0)

• (0,1)

• (0, 2)

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Leonard compared the cost of purchasing a gallon of gas at two different gas stations. The function C(g) = 3.25 + 0.07x models the average cost of a gallon of gas at the first gas station after x months. The table below shows the average cost of a gallon of gas at the second gas station after different numbers of months. Which statement is true?

• The first station had a higher initial price per gallon and increased at a greater amount per month than the second station.

• The second station had a higher initial price per gallon and increased at a greater amount per month than the first station.

• The first station had a higher initial price per gallon but increased at a smaller amount per month than the second station.

• The second station had a higher initial price per gallon but increased at a smaller amount per month than the first station.

Suppose a bacteria is introduced to two different solutions in separate petri dishes. The bacteria in the first solution grow at a rate modeled by the function G(t) = (1.40)^t. The bacteria in the second solution grow in accordance with the data displayed in the table. Which statement best describes the growth rates exhibited within the two different solutions?

• The bacteria grow at the same rate in both solutions.

• The bacteria grow at a slower rate in the first solution.

• The bacteria grow at a faster rate in the first solution.

• The bacteria decay in the first solution and grow in the second solution.

Jay earns $50 per week, plus $5.25 for each hour worked in a given week. Fred’s earnings are calculated using the formula P = 6.25(x + 8), where x is the number of hours Matt worked.

• Jay earns $2.75 per hour less than Fred.

• Fred earns $40 more than Jay for 40 hours of work.

• Jay and Fred both earn the same for 40 hours of work in a week.

• Fred earns $42 less than Jay each week when both work 0 hours.

The table below shows some of the values for the linear function f.

Let g be the linear function defined by g(x) = 4x + 5.

Which statement is true?

• The graph of f has a greater slope than the graph of g.

• The graph of g has a greater slope than the graph of f.

• The graph of f has the same slope as the graph of g.

• The slopes of the graphs of f and g are undefined.

Jasmine compared the x-intercept of f(x) = 2x – 8 to the x-intercept of the function shown in the table.

What is the value of the larger x-intercept of the two functions?

• -8

• -2

• 4

• 16

Two new cars were purchased from Frank’s Auto Yard. Car A’s value n years after its purchase is found using the function P(n) = 13,500(0.83)ⁿ. Car B’s value in different years is shown in the table.

Using an exponential model, what is the approximate difference in the percent the two cars are depreciating?

• 17%

• 10%

• 7%

• 5%