Name:_______________________________________________________ Date:_______________________________ Prd:___________
HW #25: Exponential and Logarithmic Functions
REVIEW FOR THE QUIZ (7.1-7.5): HW #25 and the Do Now!!
Part 1: Graphing Exponential Functions:
a.) Graph each exponential function below. Graph at least 2 points and the asymptote, include a table of
values and you probably want to graph the parent function as well. B.) state the domain and range!
1.)
y = 2 x+1 - 3
æ1ö
è2ø
x
2.) y = ç ÷ + 2
Part 2: Exponential Growth and Decay Modeling Problems
1.) A new car depreciates at a rate of approximately 16% per year. You bought your new car for $26,799.
Write a function that models the price of the car after t years. Then find the car’s value after the following
years (0, 1, 5, 20 years). Make a table of values.
2.) You deposit your summer earnings of $7,500 into a US Treasury Bill that pays 3% annual interest
compounded monthly. Write a function for the amount in the account after t years. How much will you
have in your account after 5 years? How much interest did you earn in 3 years?
Name:_______________________________________________________ Date:_______________________________ Prd:___________
3.) You deposit $50,000 into a high yield Swiss bank account which pays 3.5% annual interest
compounded continuously. Find the balance in the account after 10 years.
4.) The tuition at Moses Brown has been increasing by approximately 4% per year. The current tuition is
$30,000. Write a function that models the tuition at Moses Brown as a function of time. What will be the
tuition at Moses Brown in 20 years (when you decide to send your kids there)?
Challenge: How long will it take the tuition at MB to double (i.e. how many years will it take before the
tuition at MB is $60,000?
Part 3: Evaluate Logs.
Evaluate the following log without a calculator (i.e. write in exponential form and solve for x using
educated guesses). You may use the change of base formula to check your work.
a.) Log5625
b.) log 0.001
c.) log1255
d.) log21/64
Name:_______________________________________________________ Date:_______________________________ Prd:___________
Part 3: Graphing Log Functions
Graph the log function below (be sure to include at least 3 points and a table of values). State the domain
and range.
1.)
y = log2 (x – 2) + 3
2.)
Part 5: Expanding and Condensing Logs
Expand each logarithm below.
a.) log
12𝑥 7
𝑦
C.) log83xy
b.) 𝑙𝑛
7𝑥 3 𝑦 5
𝑧3
y = log1/2(x + 3)
Name:_______________________________________________________ Date:_______________________________ Prd:___________
Condense the following logarithm into a single log.
a.) 5log 𝑥 + log 𝑦 − log 10
b.) 3log 2 + log 7 − log 4
c.) ln 12 – 2 ln x
Part 6: InversesFind the inverse of the following function.
a.) f(x) = ex – 2
b.) g(x) = log5(x + 1) – 3
Part 7: Use the change of base formula to evaluate the following:
Log12500