AP Precalculus – Exponential Models – Drill 1

About This Drill

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

Practice building and interpreting exponential models of the form \( P(t) = P_0 \cdot b^t \), including doubling time, half-life, growth rate vs. growth factor, and evaluating student reasoning about exponential behavior.

Questions in This Drill

1. A car purchased for $24,000 depreciates at a rate of 15% per year. Which of the following functions models the value \( V \), in dollars, of the car \( t \) years after purchase?
2. A bacterial culture starts with 200 cells and doubles every 3 hours. Which of the following correctly represents the number of cells \( N \) after \( t \) hours?

3. t (years)	P(t)
   0	800
   1	680
   2	578
   3	491.3

   
   The table shows values of an exponential function \( P \). Which of the following is closest to the annual percent decrease represented in the table?
4. A radioactive substance has a half-life of 12 years. A sample initially contains 500 grams. Which of the following correctly represents the amount remaining, in grams, after \( t \) years?
5. A population of 1,000 animals grows according to the model \( P(t) = 1{,}000 \cdot (1.06)^t \), where \( t \) is measured in years. A student makes the following claim:
   
   "Since the growth factor is 1.06, the population increases by exactly 60 animals every year."
   
   Which of the following best evaluates the student's reasoning?