Unit 2: Exponential & Logarithmic Functions
Precalculus · Unit 2 · Paper 3

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 3” 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

Exponential growth vs decay

2

Natural log

3

Power rule for logs

4

Exponential function

5

Inverse relationship of exp and log

6

Transformations of exponentials

7

Compound interest

8

Recognizing exponential data

9

Product and quotient rules for logs

10

The number e

11

Why the base cannot be negative

12

Residuals

Short answer 1. Define or explain: Extraneous solutions

3 pts

Short answer 2. Define or explain: Semi-log plot

3 pts

Short answer 3. Define or explain: Solving logarithmic equations

3 pts

Short answer 4. Define or explain: Domain of a logarithm

3 pts

Free response

9 pts

A population of bacteria is modeled by P(t) = 500 · 2^(t/3), where t is measured in hours since the start of an experiment. (a) Find P(0) and the growth factor of the population per hour, to three decimal places. (b) Determine the exact time t at which the population reaches 8000, showing the use of logarithms. (c) The population is re-expressed in the form P(t) = 500e^(kt). Find the exact value of k and interpret it in context.