Study Guide
MATH 102 FALL 2013
REVIEW FOR THIRD EXAM
Graphing Exponential Functions - For each of the following exponential functions:
Sketch the graph of the function by first graphing the basic function and then showing one additional graph for each transformation. Label each graph with at least one point, its asymptote, and its equation.
1. 2.
3. 4.
Graphing Logarithmic Functions - For each of the following logarithmic functions:
Sketch the graph of the function by first graphing the basic function and then showing one additional graph for each transformation. Label each graph with at least one point, its asymptote, and its equation.
5. 6.
7. 8.
Using Properties of Logarithms: Express each of the following as a single logarithm and simplify:
9. 10.
11. 12.
Solving Exponential Equations - Solve each of the following.
13. 14.
15. 16.
Solving Logarithmic Equations - Solve each of the following.
17.
18.
19.
20.
Applications of Exponential Functions - Solve each of the following.
21. Salt (NaCl) decomposes in water into sodium (Na) and chloride (Cl) ions according to the law of uninhibited decay. If the initial amount of salt is 25 kilograms and, after 15 hours, 10 kilograms of salt are left,
a. Find a function, , that represents the amount of salt (in kilograms) remaining after t hours.
b. How long does it take until 20% of the initial amount of salt remains?
22. A population of bacteria obeys the law of uninhibited growth. If 600 bacteria are present initially and there are 800 after one hour,
a. Express the population P as a function of time t.
b. How long will it be until the population reaches 6600?
c. How long will it be until the population doubles?
23. A colony of bacteria increases according to the law of uninhibited growth. If the number of bacteria doubles in 4
REVIEW FOR THIRD EXAM
Graphing Exponential Functions - For each of the following exponential functions:
Sketch the graph of the function by first graphing the basic function and then showing one additional graph for each transformation. Label each graph with at least one point, its asymptote, and its equation.
1. 2.
3. 4.
Graphing Logarithmic Functions - For each of the following logarithmic functions:
Sketch the graph of the function by first graphing the basic function and then showing one additional graph for each transformation. Label each graph with at least one point, its asymptote, and its equation.
5. 6.
7. 8.
Using Properties of Logarithms: Express each of the following as a single logarithm and simplify:
9. 10.
11. 12.
Solving Exponential Equations - Solve each of the following.
13. 14.
15. 16.
Solving Logarithmic Equations - Solve each of the following.
17.
18.
19.
20.
Applications of Exponential Functions - Solve each of the following.
21. Salt (NaCl) decomposes in water into sodium (Na) and chloride (Cl) ions according to the law of uninhibited decay. If the initial amount of salt is 25 kilograms and, after 15 hours, 10 kilograms of salt are left,
a. Find a function, , that represents the amount of salt (in kilograms) remaining after t hours.
b. How long does it take until 20% of the initial amount of salt remains?
22. A population of bacteria obeys the law of uninhibited growth. If 600 bacteria are present initially and there are 800 after one hour,
a. Express the population P as a function of time t.
b. How long will it be until the population reaches 6600?
c. How long will it be until the population doubles?
23. A colony of bacteria increases according to the law of uninhibited growth. If the number of bacteria doubles in 4