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 78 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 33 min 30 points0/17 attempted
1

Recovering a from a semi-log intercept

2

Off-by-one in a sequence formula

3

Why extraneous solutions appear

4

Converting a base to a continuous rate

5

Anchor point of a logarithmic graph

6

Inverse of an exponential model

7

Why the base cannot be negative

8

Fractional exponents

9

Undoing a substitution

10

Semi-log plot

11

Exponential function

12

Why nothing exponential reaches zero

Short answer 1. Define or explain: Slope of a semi-log fit

3 pts

Short answer 2. Define or explain: −log x versus log(−x)

3 pts

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

3 pts

Short answer 4. Define or explain: Adding decibels

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.