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 78 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 33 min 30 points0/17 attempted
1

Matching bases to solve

2

Early logistic looks exponential

3

Reading a logarithmic axis

4

Geometric sequence and exponential function

5

Isolating the exponential first

6

Why perception is logarithmic

7

Log-log plot

8

Logistic model

9

Recognizing exponential data

10

Half-life independence from amount

11

Inverse of an exponential model

12

Transformations of exponentials

Short answer 1. Define or explain: Semi-log vs log-log

3 pts

Short answer 2. Define or explain: Origin of e

3 pts

Short answer 3. Define or explain: Half-life and doubling time

3 pts

Short answer 4. Define or explain: Inverse relationship of exp and log

3 pts

Free response

6 pts

A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. The population of a town is recorded every five years, as shown in the table. Time t is measured in years since the first census. t (years) 0 5 10 15 P (people) 4,200 5,100 6,200 7,500

A. An exponential regression model is used to fit these data. Give the equation of that model in the form P(t) = a·b^t, with a and b rounded to four decimal places where appropriate, and interpret the value of b in context.

B. Use the model to predict the population 25 years after the first census. Show the setup for your calculation.

C. Use the model to determine the year in which the population first reaches 10,000. Give your answer to three decimal places, and explain one reason the prediction should be treated with caution.