Here are the steps to solve this compound interest problem: * Principal (P) = $1000 * Annual interest rate (r) = 9% = 0.09 * Number of interest periods per year (n) = 12 (monthly) * Interest is compounded monthly * Calculate amount after 5 years, 10 years, and 15 years using the compound interest formula: 5 years: A = 1000(1 + 0.09/12)^(12*5) = $1581.53 10 years: A = 1000(1 + 0.09/12)^(12*10) = $2501.04 15 years: A = 1000(1 + 0.09/12

1. Day 16
1. Opener
Sketch the graph of f(x) = (1/2)x.

2. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.

3. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.

4. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.

5. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.

6. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x

7. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y

8. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2

9. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2
-1

10. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2
-1
0

11. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2
-1
0
1

12. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2
-1
0
1
2

13. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2 4
-1
0
1
2

14. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2 4
-1 2
0
1
2

15. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2 4
-1 2
0 1
1
2

16. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2 4
-1 2
0 1
1 1/2
2

17. Day 16
1. Opener
0<a<1
Sketch the graph of f(x) = (1/2)x.
x y
-2 4
-1 2
0 1
1 1/2
2 1/4

18. Day 17
1. Opener
Find the exact value of
a) log 2 8
1
b) log 3
3
c) log 5 25

19. Day 17
1. Opener
Find the exact value of
a) log 2 8 =3
1
b) log 3
3
c) log 5 25

20. Day 17
1. Opener
Find the exact value of
a) log 2 8 =3
1
b) log 3 = -1
3
c) log 5 25

21. Day 17
1. Opener
Find the exact value of
a) log 2 8 =3
1
b) log 3 = -1
3
c) log 5 25 =2

22. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5
b) log e b = −3
c) log 3 5 = c

23. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5 a5 = 4
b) log e b = −3
c) log 3 5 = c

24. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5 a5 = 4
b) log e b = −3 e-3 = b
c) log 3 5 = c

25. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5 a5 = 4
b) log e b = −3 e-3 = b
c) log 3 5 = c 3c = 5

26. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5
b) log e b = −3
c) log 3 5 = c

27. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5 a5 = 4
b) log e b = −3
c) log 3 5 = c

28. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5 a5 = 4
b) log e b = −3 e-3 = b
c) log 3 5 = c

29. Change each logarithmic expression to an
equivalent expression containing an exponent.
a) log a 4 = 5 a5 = 4
b) log e b = −3 e-3 = b
c) log 3 5 = c 3c = 5

30. 2. Graphs of Logarithmic functions.
y = loga x

31. 2. Graphs of Logarithmic functions.
Sketch the graph of the function below
Find the domain and range.
y = log 2 ( x + 2 )

32. 2. Graphs of Logarithmic functions.
Sketch the graph of the function below
Find the domain and range.
y = log 1 ( x ) − 2
3

33. 2. Graphs of Logarithmic functions.
Sketch the graph of the function below
Find the domain and range.
y = log 3 ( x + 1) − 2
2

34. 3. Exercises.
Sketch the graph of the functions below
Find the domain and range.
1. f (x) = ln ( x + 4 )
2. f (x) = − log x
3. g(x) = log 2 ( x − 3) + 2
3
4. h(x) = log 3 ( x − 4 ) + 3
5. y = log 4 ( x + 1) − 2
3

35. Day 18
1. Opener
Solve the equation
a) 7 x+6 = 7 3x−4
2 x+3 x2
b) 3 =3
−100 x x−4
c) 2 = ( 0.5 )
d) 4 x−3 = 8 4−x
3−2 x
⎛ 1 ⎞ x 2
x
e) 4 ⋅ ⎜ ⎟ = 8 ⋅(2 )
⎝ 2 ⎠

36. Day 18
1. Opener
Solve the equation
a) 7 x+6 = 7 3x−4 =5
2 x+3 x2
b) 3 =3
−100 x x−4
c) 2 = ( 0.5 )
d) 4 x−3 = 8 4−x
3−2 x
⎛ 1 ⎞ x 2
x
e) 4 ⋅ ⎜ ⎟ = 8 ⋅(2 )
⎝ 2 ⎠

37. Day 18
1. Opener
Solve the equation
a) 7 x+6 = 7 3x−4 =5
2 x+3 x2 = -1, 3
b) 3 =3
−100 x x−4
c) 2 = ( 0.5 )
d) 4 x−3 = 8 4−x
3−2 x
⎛ 1 ⎞ x 2
x
e) 4 ⋅ ⎜ ⎟ = 8 ⋅(2 )
⎝ 2 ⎠

38. Day 18
1. Opener
Solve the equation
a) 7 x+6 = 7 3x−4 =5
2 x+3 x2 = -1, 3
b) 3 =3
x−4
c) 2 −100 x
= ( 0.5 ) = -4/99
d) 4 x−3 = 8 4−x
3−2 x
⎛ 1 ⎞ x 2
x
e) 4 ⋅ ⎜ ⎟ = 8 ⋅(2 )
⎝ 2 ⎠

39. Day 18
1. Opener
Solve the equation
a) 7 x+6 = 7 3x−4 =5
2 x+3 x2 = -1, 3
b) 3 =3
x−4
c) 2 −100 x
= ( 0.5 ) = -4/99
d) 4 x−3 = 8 4−x = 18/5
3−2 x
⎛ 1 ⎞ x 2
x
e) 4 ⋅ ⎜ ⎟ = 8 ⋅(2 )
⎝ 2 ⎠

40. Day 18
1. Opener
Solve the equation
a) 7 x+6 = 7 3x−4 =5
2 x+3 x2 = -1, 3
b) 3 =3
x−4
c) 2 −100 x
= ( 0.5 ) = -4/99
d) 4 x−3 = 8 4−x = 18/5
3−2 x
⎛ 1 ⎞ x 2
x
e) 4 ⋅ ⎜ ⎟ = 8 ⋅(2 ) =3
⎝ 2 ⎠

41. 2. Solving a logarithmic equation
Solve the equation
log 4 ( 5 + x ) = 3

42. 2. Solving a logarithmic equation
Solve the equation
log 6 ( 4x − 5 ) = log 6 ( 2x + 1)

43. 2. Solving a logarithmic equation
The population N(t) (in millions) of the United States t
years after 1980 may be approximated by the formula
N(t) = 227e0.007t. When will the population be twice what
it was in 1980?

44. 3. Compound Interest Formula
nt
⎛ r ⎞
A = P ⎜ 1+ ⎟
⎝ n ⎠
where
P = Principal
r = annual interest rate expressed as a decimal
n = number of interest periods per year
t = number of years P is invested
A = amount after t years

45. 3. Compound Interest Formula
Suppose that $1000 is invested at an interest rate of 9%
compounded monthly. Find the new amount of principal
after 5 years, after 10 years, and after 15 years. Illustrate
graphically the growth of the investment.