Unit 2: Exponential & Logarithmic Functions
Precalculus · Unit 2 · Paper 2

Exponential & Logarithmic Functions unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 30 terms and is the same for everyone, so a teacher can assign “Unit 2, Paper 2” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 36 min 33 points0/17 attempted
1

Fractional exponents

2

Inverse of an exponential model

3

Power rule for logs

4

Newton's law of cooling

5

Half-life and doubling time

6

Extraneous solutions

7

Solving exponential equations

8

The number e

9

Change of base formula

10

Domain of a logarithm

11

Compound interest

12

Solving logarithmic equations

Short answer 1. Define or explain: Log-log plot

3 pts

Short answer 2. Define or explain: Exponential vs power function

3 pts

Short answer 3. Define or explain: Residuals

3 pts

Short answer 4. Define or explain: Logarithm definition

3 pts

Free response

9 pts

A population of bacteria in a culture is modeled by P(t) = 400·(1.35)^t, where P is measured in thousands of cells and t is measured in hours since the culture was prepared.

Determine the initial population and the hourly percent rate of increase.

Find the time at which the population reaches 2,000 thousand cells. Give an exact expression and a decimal approximation to three places.

Determine the average rate of change of P over the interval from t = 0 to t = 5, with units.

A second culture is modeled by Q(t) = 400 + 540t. Explain which model predicts a larger population at t = 10 and why the difference grows with t.