Comparing Slopes of Different Functions

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.

What is the approximate difference in the growth rates of the two functions?

• 0%

• 3%

• 5%

• 8%

Which statement about the two accounts is true?

• Valerie initially invested $1 more than Kaylee.

• Kaylee initially invested $2 more than Valerie.

• Kaylee’s account is receiving an annual rate of 1 percentage point greater than Valerie’s account.

• Valerie’s account is receiving an annual rate of 2 percentage points greater than Kaylee’s account.

The function C(m) = 0.55m + 3.75 models the cost to take an m mile-long taxi ride from Quick Cabs. The table shows the cost to take a cab different distances from Get You There Cabs. Which statement is true about the two cab companies?

• Quick Cabs costs less per mile but has a higher fixed fee than Get You There Cabs.

• Quick Cabs costs more per mile but has a lower fixed fee than Get You There Cabs.

• Quick Cabs costs less per mile and has a lower fixed fee than Get You There Cabs.

• Quick Cabs costs more per mile and has a higher fixed fee than Get You There Cabs.

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%

Kyle sells bags of popcorn at school events. The function P = 1.25b – 18 represents Kyle’s profit, where P stands for profit and b stands for the number of bags of popcorn sold. His brother Nathan sells bottles of fruit juice and has kept track of his daily sales and profit in the table. If Nathan’s profit is modeled linearly, which statement can be predicted from the two models?

• Kyle will have a higher profit than Nathan if they each sell 50 items.

• Kyle will have a higher profit than Nathan if they each sell 40 items.

• Kyle will have a higher profit than Nathan if they each sell 30 items.

• Kyle will have a higher profit than Nathan if they each sell 20 items.

Which function has a greater slope? (Hint slope is Y / X)

• Function A

• Function B

• Function C

Which statement below is true? (Hint slope is Y / X)

• The slope of Function A is greater then the slope of Function B

• The slope of Function A is less than the slope of Function B

• The slope of Function A is the same as the slope of Function B

Function A and B are linear Functions. Which statement below is true? (Hint slope is Y / X)

• The slope of Function A is greater than the slope of Function B

• The slope of Function A is less than the slope of Function B

• The slope of Function A is the same as the slope of Function B

Which Function has a greater slope? (Hint slope is Y / X)

• Smith has the greater rate of change with 5/4

• Smith has the greater rate of change with 4/5

• Harmon has the greater rate of change with 7/2

• They have the same rate of change.