Algebra 2H
Mathematician: ___________________________________
7.1_7.3 Review
Graphing Exponential Functions
Graph and state the domain, range, asymptote and y intercept of:
𝑓(𝑥) = 2𝑥+2 + 1
1
𝑔(𝑥) = −(2)𝑥−2 − 2
Graphing Logarithmic Functions
Graph and state the domain, range, asymptote and x intercept of:
𝑓(𝑥) = −𝑙𝑜𝑔3 (𝑥 − 2)
𝑔(𝑥) = 2𝑙𝑜𝑔4 (𝑥 + 3) + 1
Evaluating Logarithms
1
7
1) log 2 32
2) log9 27
3) log10 (0.001)
4) log6 1
5) log 7 3
6) log 1 9
7) log 4 5 4
8) log36 6
9) log5 25 5
10) log5
1
125
12) log 7 7
13) log16 2
14) log5 3 25
15) log 3
1
9
18) 𝑥 log𝑥 72
19) (log2(log381)
3
11) log 4 16
16) 12log12 144
17) 5log5 17
21) 𝑙𝑜𝑔4 43
Writing Inverses- Find the inverse of each function
22) 𝑓(𝑥) = 4𝑥 − 1
23) 𝑓(𝑥) = 5𝑥 3 + 1
26) 𝑓(𝑥) = 2𝑥 + 1
27) 𝑓(𝑥) = log(𝑥 − 6)
24) 𝑓(𝑥) = √𝑥 + 6
25) 𝑓(𝑥) = (𝑥 + 3)2
Growth and Decay Word Problems
28) The half-life of radium is 1690 years. If 10 grams are present now, how much will be present in 50 years?
29) While you are waiting for your tennis partner to show up, you drop your tennis ball from 5 feet. Its
rebound was approximately 35 inches on the first bounce and 21.5 inches on the second. What exponential
model would be a good model for the bouncing ball?
Interest Word Problems –
𝑟
𝐴(𝑡) = 𝑃(1 + )𝑛𝑡
𝑛
𝐴(𝑡) = 𝑃𝑒 𝑟𝑡
30) Find the amount of money that results if $100 is invested at 4% compounded quarterly for 2 years.
31) A sum of $1500 was invested for 5 years, and the interest was compounded monthly. If this sum amounted
to $1633 in the given time, what was the interest rate?
32) Find the amount of money that results if $100 is invested at 10% compounded continuously for 2.25 years.
33) Find the principal needed to get $1000 after 1 year at 12% compounded continuously.
34) The initial value of a car is $25000. After one year, the value of the car is $21,250. Write an exponential
function to model the expected value of the car. Estimate the value of the car after 5 years.
Cooling problem
35) ) A pizza baked at 450°F is removed from the oven at 5pm into a room that is a constant 70°F.
After 5 minutes, the pizza is at 300°F. At 10 min., 200°F. At 20 min it is 89°F. Write an exponential
equation to model the data. At what time can you begin eating pizza if you want its temperature to be
135°?
Logarithmic Scale
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that
𝐼
earthquake to the intensity level of each earthquake below. Remember 𝑙𝑜𝑔 𝐼1 = 𝑀1 − 𝑀2
2
36) magnitude 7.7 in San Francisco, California, in 1906.
37) magnitude 9.5 in Valdivia, Chile, in 1960.