Unit 2: Exponential & Logarithmic Functions
Precalculus · Unit 2 · Paper 1

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 1” 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 30 min 27 points0/17 attempted
1

Exponential function

2

Inverse relationship of exp and log

3

Natural log

4

Residuals

5

Power rule for logs

6

Logistic model

7

The number e

8

Change of base formula

9

Semi-log plot

10

Extraneous solutions

11

Inverse of an exponential model

12

Horizontal asymptote of an exponential

Short answer 1. Define or explain: Logarithm definition

3 pts

Short answer 2. Define or explain: Fractional exponents

3 pts

Short answer 3. Define or explain: Solving exponential equations

3 pts

Short answer 4. Define or explain: Common modeling error

3 pts

Free response

3 pts

The population of a species of fish in a lake is modeled by the logistic function P(t) = 1200 / (1 + 15e^(-0.2t)), where t is the number of years since the lake was stocked.

Determine the initial population of the fish.

Find the carrying capacity of the lake for this species.

At what time t is the population growing the fastest?