AP Precalculus Function Model Selection Drill 1

About This Drill

AP Precalculus Function Model Selection Drill 1 is a Math practice drill covering Function Model Selection. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice selecting the best function model — linear, quadratic, exponential, or rational — given data tables and real-world contexts. These questions reflect the reasoning skills assessed in Topics 1.13–1.14 of AP® Precalculus.

Questions in This Drill

1. The table below shows values of a function f.
   
   

   x	0	1	2	3	4
   f(x)	3	6	12	24	48

   
   Which of the following best justifies that f is best modeled by an exponential function?
2. The table below shows values of a function g.
   
   

   x	0	1	2	3	4
   g(x)	2	5	10	17	26

   
   Which of the following best describes the function type that models g?
3. A population of bacteria doubles every 3 hours. At time t = 0, there are 500 bacteria. Which of the following correctly expresses the number of bacteria after t hours?
4. The table below shows the value V (in dollars) of a car t years after purchase.
   
   

   t	0	1	2	3	4
   V(t)	24,000	19,200	15,360	12,288	9,830

   
   Which of the following best describes the function type that models V, and what feature of the table justifies this choice?
5. A company’s monthly revenue R (in thousands of dollars) over the first several months is shown in the table below.
   
   

   Month (t)	1	2	3	4	5
   R(t)	4	7	11	16	22

   
   A student concludes: “Because the revenue is always increasing and the rate of increase is also increasing, the data must be modeled by an exponential function.” Is the student’s conclusion correct?