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 78 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 33 min 30 points0/17 attempted
1

Asymptote of a transformed exponential

2

Geometric sequence and exponential function

3

Anchor point of a logarithmic graph

4

Converting a base to a continuous rate

5

Solving logarithmic equations

6

Exponent rules

7

Extraneous solutions

8

Recognizing exponential data

9

Arithmetic sequence and linear function

10

Counting half-lives

11

Logarithm definition

12

Power rule for logs

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

3 pts

Short answer 2. Define or explain: Why e is the natural base

3 pts

Short answer 3. Define or explain: Adding decibels

3 pts

Short answer 4. Define or explain: Matching bases to solve

3 pts

Free response

6 pts

A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. A cup of coffee is poured in a room held at a constant temperature. The temperature of the coffee, in degrees Celsius, is modeled by T(t) = 22 + 58e^(−0.09t) where t is the number of minutes since the coffee was poured.

A. Find the initial temperature of the coffee, and determine the temperature the coffee approaches as t increases without bound. Explain what that limiting value represents.

B. Find the time at which the temperature of the coffee is 50 degrees Celsius. Give your answer to three decimal places.

C. Find the average rate of change of T over the interval 0 ≤ t ≤ 10, with units. Then rewrite the model in the form T(t) = 22 + 58b^t and interpret the value of b in context.