Show:
Laws of Exponents
Properties of Exponential Functions
Solving Exponential Equations
Logarithm to Exponential and back Again
Potpourri
100
Simplify (4^7)*(4^20)*(4^0) =
4^27
100
1, 2, 4, 8, 16, 32, 64...What type of growth pattern is this?
Exponential Growth
100
Solve for m [4^(2m)] = [4^(m+1)]
m = 1
100
Rewrite in exponential form log base 5 of 625 = 4
5^4 = 625
100
What is the difference between -1^2 and (-1)^2 ?
-1^2 is -1 but (-1)^2 is 1
200
Simplify [a*(b^2)*a^4]^15
(a^75)*(b^30)
200
What is the y-intercept of y = [4^(x-2)] + 3/16
1/4
200
Solve for y. [3^(7y-2)] = 3*[3^(-y+4)]
y = 7/8
200
Rewrite in log form 8^3 = 512
log base 8 of 512 = 3
200
Factor completely 5x^3 + 15x^2 - 20x - 60
5(x^2-4)*(x+3)
300
What is the purpose of applying the laws of exponents?
To simplify a problem and/or combine like terms
300
Name 3 applications of exponentials for modeling.
Many answers will work. Examples: radioactive decay, compound interest, population growth, disease spread
300
Solve for x [5^(x+3)]/25 = 125^x
x = 1/2
300
Evaluate the following log base 3 of 3^4 + log base 4 of 64 - log base 4 of 4
6
300
What is the end behavior of f(x)? f(x) = (12x^5 + 4x^4 - 3)/(9x^3 + 6x +2)
f(x) goes to infinity as x goes to +/- infinity
400
Evaluate the following: 32^(3/5)
8
400
What is the y-intercept of y = (e^x) + 3
4
400
[32^(x-4)]^2 = (64^x)*16
x = 11
400
Evaluate [(e^ln6)*(e^ln8)]
48
400
What is the maximum number of turning points the polynomial can have? h(x) = 9x^6 - 12x + 8
5
500
Prove that {[(x^7)*y*(z^5)]/[(x^4)*(y^3)]}^2 = [(x^6)*(z^10)]/(y^4)
To be shown
500
What does "e" stand for?
Any of the following will work: Euler's number the natural base the natural number 2.718281828...
500
[81^(x+2)]*[9^(5x-2)]/(27*3) = [243^x]^(x-8)
x = 0 x = 54/5
500
Evaluate the following: 32^(log base 2 of 3)
243
500
What does the following sequence produce? [n(n+1)]/2 where n is (1, 2, 3, 4, 5, ...)
the odd numbers