7.1-7.6 Review (Omitting 7.4)
1 x
(3)
2
a) Graph by using a table.
2. y  4(.75) x
b) Is this exponential growth
or decay? Why?
b) Is this exponential growth
or decay? Why?
c) What is the asymptote?
c) What is the asymptote?
d) What is the key point?
d) What is the key point?
1. y 
a) Graph by using a table.
***Note: The key point began at (0, 1). Where is that point now?
Compare the function to its parent graph (no graphing calculator)
3. y  (5) x 3
4. y  2(5) x  7
5. y 
1 x
(5)  9
2
6. y 
2 x 1
(5)  3
3
Graph the parent function and then the transformation function using at least three
points. Clearly identify the horizontal asymptote.
7) f ( x)  5
x
1
8) f  x     4
2 
x 1
1
9) f ( x)  (2) x +3
4
1
11) f ( x)    
3
x
1
10) f ( x)   
4
x2
5
Write an equation and then solve. Make sure you pick the correct formula!!!
12. A new car that sells for $18,000 depreciates 25% each year. Write a function
that models the value of the car. Find the value of the car after 4 yrs. Round to the
nearest cent.
13. The bear population increases at a rate of 2% each year. There are 1574 bears
this year. Write a function that models the bear population. How many bears will
there be in 10 yrs? Round to the nearest whole number.
.
14. Colin deposited $950 in an account that compounded continuously over 10 yrs.
If the annual interest is 6.5%, find the amount in the account. Round to the nearest
cent.
15. A total of $12,000 is invested at an annual percentage rate of 9%. Find the
balance after five years if it is compounded continuously. Round to the nearest
cent.
16. Savannah wants to save $8000 for college in five years. How much should be
put into an account that earns 5.2% annual interest compounded continuously?
Round to the nearest cent.
Write each equation in logarithmic form.
17. 92 = 81
18.
1 æ1ö
=ç ÷
64 è 4 ø
3
19. 83 = 512
-2
1
20. æç ö÷ = 9
3
è ø
Evaluate each logarithm.
21. log 2 128
22. log 100,000
23. log 2 (-32)
24. log 3
1
81
In 2004, an earthquake of magnitude 7.0 shook Papua, Indonesia. Compare
the intensity level of that earthquake to the intensity level of each
earthquake below.
25. magnitude 6.1 in Costa Rica, in 2009
26. magnitude 5.1 in Greece, in 2008
Graph each logarithmic function.
27. y = log x
28. y = log3 x
Describe how the graph of each function compares with the graph of the parent function, y = log b x
29. y = log3 x - 2
y = log 2 ( x - 4) + 1
30. y = log8 (x - 2)
31. y = log6 ( x + 1) - 5
32.
Solve each equation. Round answers to the nearest hundredth.
33. 82 x = 32
34. 7n = 343
37. 36-2 x +1 = 216
36. 252 n+1 = 625
38. 52 x = 20
35. 92 x = 27
39. 8n+1 = 3
40. 4x − 5 = 12
Solve each equation. Check your answers.
41. log x = 2
42. log 4x = − 1
43. log 3x = 2
44. log 4x = 2
45. log (2x + 5) = 3
46. 8 log x = 16
Solve each equation. Check your answers. Round your answer to the nearest
hundredth.
47. 4 ln x = 2
48. ln (3x  4) = 7
Use natural logarithms to solve each equation. Round your answer to the nearest
hundredth.
49. ex = 15
50. 4ex = 10
51. 5e6x+3 = 0.1
52. ex+ 6 + 5 = 1