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Exponential and Logarithmic Functions
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f(x) = 2 (5/2)^x Is this a growth or decay function? Why?
f(x) = 2 (5/2)^x Is this a growth or decay function? Why?
Growth 5/2 > 1
f(x) = (0.8)^x Is this a growth or decay function? Why?
f(x) = (0.8)^x Is this a growth or decay function? Why?
Decay 0.8 < 1
A motor scooter purchased for $1000 depereciates at an annual rate of 15%. Write an exponential function.
A motor scooter purchased for $1000 depereciates at an annual rate of 15%. Write an exponential function.
A(t) = 1000(0.85)^t
A rare coin is valued at $5.00. If it appreciates at a rate of 12.5 % per year, how much will it be worth in 20 years?
A rare coin is valued at $5.00. If it appreciates at a rate of 12.5 % per year, how much will it be worth in 20 years?
A(t) = 5(1.125)^20 = $52.73
How do you know to use (1+ r) or (1-r)
How do you know to use (1+ r) or (1-r)
1+r is for growth, 1-r is for decay
What are the steps to finding an inverse function?
What are the steps to finding an inverse function?
1) replace f(x) w/y. 2) Switch x and y. 3) Solve for y. 4) Write f^-1(x).
Find the inverse of f(x) = 2x
Find the inverse of f(x) = 2x
f^-1(x) = x/2
Find the inverse of f(x) = x/4 - 5
Find the inverse of f(x) = x/4 - 5
f^-1 (x) = 4x + 20
If a function has values x = -1, 0, 3 and y = 5, 7, 2 find the inverse function.
If a function has values x = -1, 0, 3 and y = 5, 7, 2 find the inverse function.
x = 5, 7, 2 and y = -1, 0, 3
If you have a graph describe how to find the inverse.
If you have a graph describe how to find the inverse.
Reflect the graph over the line y = x or switch the x and y values
Rewrite 2^6 = 64 in log form.
Rewrite 2^6 = 64 in log form.
Log2 (64) = 6 (note: 2 is the base)
Rewrite Log 10,000 = 4 in exponential form
Rewrite Log 10,000 = 4 in exponential form
10^4 - 10,000
Log 0.5 (0.5) = (note: 0.5 is the base)
Log 0.5 (0.5) = (note: 0.5 is the base)
1
Log 1
Log 1
0
Log 4 (1/4) (note: 4 is the base)
Log 4 (1/4) (note: 4 is the base)
-1
Log 5 (625) + Log 5 (25) (note: 5 is the base)
Log 5 (625) + Log 5 (25) (note: 5 is the base)
6
Log 7 (49 ) - Log 7 (7) (note: 7 is the base)
Log 7 (49 ) - Log 7 (7) (note: 7 is the base)
1
Log 3 (81^2) (note: 3 is the base)
Log 3 (81^2) (note: 3 is the base)
8
Log 2 (1/2 ^5) (note: 2 is the base)
Log 2 (1/2 ^5) (note: 2 is the base)
-5
Use change of base to find log 9 (27) (note: base is 9)
Use change of base to find log 9 (27) (note: base is 9)
1.5
Solve 3^2x = 27
Solve 3^2x = 27
1.5
Solve 3 = Log 8 + 3Logx
Solve 3 = Log 8 + 3Logx
5
Solve 2Log x - Log 4 = 0
Solve 2Log x - Log 4 = 0
2
Solve Log x + Log (x + 9) = 1
Solve Log x + Log (x + 9) = 1
1 because -10 is not possible
Solve log 3 (x-5) = 2 (note: 3 is the base)
Solve log 3 (x-5) = 2 (note: 3 is the base)
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What Would You Like To Risk?
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Go To The Final Question
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Edit This Game:
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