Name __________________________ Date _____ Per. ______ Ms. Williams/Mrs. Hertel
Day 7: Solving Exponential Word Problems involving Logarithms
Warm – Up
Exponential growth occurs when a quantity increases by the same rate r in each period t.
When this happens, the value of the quantity at any given time can be calculated as a function
of the rate and the original amount.
Exponential decay occurs when a quantity decreases by the same rate r in each time period t.
Just like exponential growth, the value of the quantity at any given time can be calculated by
using the rate and the original amount.
In Summary,
Example 1: “Growth”
The original value of a painting is $9,000 and the value increases by 7% each year.
Part a: Then find the painting’s value in 15 years.
Part b: In what year, will the painting be worth $50,000?
Example 2: “Decay”
The population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people.
Part a: Find the population in 2012.
Part b: In what year, will the population be double?
3) Is the equation A = 3200 (0.70)t
a model of exponential growth or exponential decay, and what is the rate
(percent) of change per time period?
Explain here!
1) exponential growth and 30%
2) exponential growth and 70%
3) exponential decay and 30%
4) exponential decay and 70%
4) Is the equation A = 1756 (1.17)t a model of exponential growth or exponential decay, and
what is the rate (percent) of change per time period?
Explain here!
1) exponential growth and 17%
2) exponential growth and 83%
3) exponential decay and 17%
4) exponential decay and 83%
5)
Graphs of Logarithmic Functions
Using the table below: a) Complete the table of values for y= 2x
b) sketch the graph of y= 2x
x
y
-2
-1
0
1
2
2) Recall:
How do we find the inverse of a function?
Find the inverse algebraically.
3) Graph the inverse of the function y = 2x.
Properties of
Properties of
Domain:
Domain:
Range:
Range:
Asymptote:
Asymptote:
x-intercept:
x-intercept:
y-intercept:
y-intercept:
Rule for Graphing Exponential Functions
Rule for Graphing Log Functions
x
y
x
y
-1
1
𝑏
1
𝑏
−1
0
1
1
0
1
𝑏
b
1
5.
6.
Exit Ticket
Word Problems Homework Day 1
Write an exponential growth/ decay function to model each situation. Then find the value of the function after the
given number of years.
1)
2)
3)
4) Is the equation A = 10,000 (0.45)t
a model of exponential growth or exponential decay, and what is the rate
(percent) of change per time period?
1) exponential growth and 45%
Explain here!
2) exponential growth and 55%
3) exponential decay and 45%
4) exponential decay and 55%
5) Is the equation A = 5400 (1.07)t
a model of exponential growth or exponential decay, and what is the rate (percent)
of change per time period?
1) exponential growth and 7%
2) exponential growth and 93%
3) exponential decay and 7%
4) exponential decay and 93%
Explain here!
6)
7) Sketch below the graph of
asymptote.
8)
. Then, state the domain and range of the graph. Write the equation of the
Name __________________________ Date _____ Per. ______ Ms. Williams/Mrs. Hertel
Day 8: Solving Exponential Word Problems involving Logarithms
Warm – Up
1) In January 1995, the population of a small town was 8,000 people. Each year after
1995, the population decreased by 1%.
a. Find the population of the town in January 2000.
b. If this rate of decrease continues unchanged, what is the expected population of the
town in January 2010?
2)
Example 1: “Level A”
Example 2: “Level B”
Example 3: “Level A”
Example 4: “Level B”
Regents Question & Exit Ticket
Summary
Exit Ticket
Day 8 – Homework
1)
2)
3)
4)
5)
6)
7)
8)
9)
NAME:________________________________________
Algebra 2/Trig – Unit 10: Logarithms REVIEW SHEET
Converting and Solving Logarithms
1. Solve for x: log 3 (x - 1) = 2
2. Find the value of
DATE:_________
PERIOD:_______
5. Solve for x to the nearest hundredth:
to four decimal places.
Using the Power Law
6. Solve for x to the nearest thousandth:
3. The relationship between the relative size of
an earthquake, S, and the measure of the
earthquake on the Richter scale, R, is given
by the equation log S = R. If an earthquake
measured 6.2 on the Richter scale, what was
its relative size to the nearest tenth?
7. Using logarithms, find w to the nearest tenthousandth:
4. The expression
1) 8
2) 2
3)
4)
is equivalent to
Product and Quotient Laws
8. The expression
1)
2)
is equivalent to
3)
10. If
Substitution with Logarithms
and
, what is
√ ?
(1) x  2 y
(2) 2 x  2 y
4)
11. Given:
x y
2
y
(4) x 
2
(3)
and
Express in terms of p and q:
9. The expression
( ) is equivalent to
√
1)
2)
3)
4)
Solving Logarithmic Equations
12. Solve algebraically for all values of x:
13. Solve for x:
Undefined Logarithms
14. The expression log (x - 4) is defined for all values of x such that
(1) -2 ≤ x ≤ 2
(3) x ≥ 2 or x ≤ -2
(2) -2 < x < 2
(4) x > 2 or x < -2
2
Solving Logarithmic Word Problems
15. The scientists in a laboratory company raise amebas to sell to schools for use in biology classes. They
know that one ameba divides into two amebas every hour and that the formula t = log 3 N can be used to
determine how long in hours, t, it takes to produce a certain number of amebas, N. Determine, to the
nearest hundredth of an hour, how long it takes to produce 5,000 amebas if they start with one ameba.
16. Sean invests $10,000 at an annual rate of 5% compounded continuously, according to the formula
A  Pert , where A is the amount, P is the principal, r is the rate of interest, and t is time, in years.
Determine, to the nearest dollar, the amount of money he will have after 2 years.
Determine how many years, to the nearest year, it will take for his initial investment to double.
Inverse and Graphs of Logarithms
17. What is the inverse of the function y = log 3 x
(1) 3 y = x
(2) 3 x = y
(3) x 3 = y
(4) y = x 3
18. Graph the equations
on the same set of axes. State the domain and range of
Write the equation of the asymptote of
.
.