Comparing Functions

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.

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.

Jason invested money into two different accounts. He deposited $75 into the first account which earns 6% interest annually. The value of the second account after different amounts of time is shown in the table.

Which statement is true?

• Jason started with $4 less in the second account than the first account.

• Jason started with $5 less in the second account than the first account.

• Jason started with $4 more in the second account than the first account.

• Jason started with $5 more in the second account than the first account.

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.

Which statement is true?

• 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%

The function f(x) = 14,000(1.3)^x models the population of of town 1 x years after January 2006. The table below shows the population of town 2 in different years.

Assuming both towns continue to grow at the same rate, which statement is true?

• Town 1 had a greater population than town 2 in 2006 and is growing at a faster rate than town 2.

• Town 2 had a greater population than town 1 in 2006 and is growing at a faster rate than town 1.

• Town 1 had a greater population than town 2 in 2006, but is growing at a slower rate than town 2.

• Town 2 had a greater population than town 1 in 2006, but is growing at a slower rate than town 1.

Two exponential functions are shown .

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

• 0%

• 3%

• 5%

• 8%

A scientist is observing the population of rabbits in two different areas of the state.

-- The function f(x) = 9,620(0.84)^x models the population of rabbits in the western part of the state x years after the scientist began his observations.

-- The table shows the population of rabbits in the eastern part of the state after different amounts of time.

Which statement is true?

• Both rabbit populations are changing in size at the same rate.

• The eastern population of rabbits is changing in size at a faster rate than the western population.

• Both rabbit populations had the same initial population.

• The eastern population of rabbits had a greater initial population than the western population.