1. Exam 3 - Chapters 10 and 11 REVIEW
Key Words to Know:
exponent:
exponential function:
logarithmic function:
“common” logarithmic function:
growth factor:
decay factor:
growth rate:
decay rate:
doubling time:
half-life:
Key Formulas to Know:
a • bⁿ
b=r+1
logᵦ a = x
logᵦ a = x Bᵡ = a

2. Review of Exponent/Logarithmic Laws:
1.
2.
3.
4.
5.
6.
7.
8.

3. What do the graphs of the following functions look like and what are the limitations of
each:
a. exponentially growing function:
b. exponentially decaying function:
c. logarithmic function:
Exponential Problem Practice:
Write and expression and solve for the following:
The quantity of pollutant remaining in a lake if it is removed at 2% a year
for 5 years.

4. A population at time t years if it is initially 2 million and growing at 3% each
year. If the population was 2 million in 2012, what would the population in
2020?
Without a calculator solve the following:
a. 144 = 12ᵡ
b. 50 = 5 • 10⁽ᵡ⧶²⁾
c. Given that formulas I - III all describe the growth of the same population,
with time, t, in years:
I. P = 15(2)⌃(t/6)
II. P = 15(4) ⌃(t/12)
III. P = 15(16) ⌃(t/24)
Show that the three formulas are equivalent:
What does formula I tell you about the doubling time of the population?
What do formulas II and III tell you about the growth of the population?

5. Solving Exponential Problems Using Logarithms:
1. 10ᵡ = 421
2. 10ᵡ = 3/√(17)
3. You deposit $10,000 into a bank account. Use the annual interest rate given to
find the doubling time or half-life of the account.
a. 2% interest
b. -.05% interest