### Simplify each of the following using the laws of exponents

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A+ TUTORIAL FOR THE FOLLOWING QUESTIONS

1. Simplify each of the following using the laws of exponents

a) ((9)^(1/2)^2)/24

b) 16^(x+2)

c) 3^(-8)/(3^(-6)^(-5) )

d) (4^(-2)+2^(-4) )^(-1)

1. Simplify each of the following.

a) (x^(a-b) )^(a+b)/x^(b^2 )

b) ?((x^(1/4) ?x)/?(5&x^2 ))

c) (ab)^(2x+y)/(a^x b^y )

1. Sketch a graph of a function and show a secant line and a tangent line to this function.

2. Prove: 2^n+2^n=2^(n+1)

3. Complete the following:

a. Find the slope of the secant to the curve f(x) = 0.25(4)^x 2 between:

i. x = 0 and x = 1

ii. x = 0 and x = 0.5

iii. x = 0 and x = 0.1

iv. x = 0 and x = 0.01

b. Extend the result from part a) to determine the slope of the tangent to the curve at x = 0 accurate to 3 decimal places.

1. For the curve y = 3(1/2)^x 1, determine the following:

a. the horizontal asymptote

b. the y-intercept

c. the domain and range

d. sketch a curve

1. An antique dresser was purchased for \$7500 in 2005. The dresser increases in value by 9% per year. Find the value of the dresser in 2025.

2. If a bacteria population doubles in 7 days, when was it half of its present population?

3. The value of a new car depreciates at a rate of 12% per year.

a. Write an equation to represent the approximate value of a car purchased for \$23000.

b. Determine the value of the car two years after it is purchased.

c. Approximately how many years will it take until the car is worth \$2300?

1. Beginning with the function f(x)=(0.8)^x, state what transformations were used on this to obtain the functions given below:

a. g(x) = -(0.8)^x 2

b. h(x) = (0.8)^(x-2)

c. k(x) = (0.8)^(-3x+9)

1. Inflation is currently causing the cost of items to increase by about 2.5% per year. In 2009 a litre of gasoline costs approximately \$0.90. What will it cost to fill a 60 litre gas tank 10 years from now? Round your answer to the nearest dollar. Name at least one thing other than inflation that determines the cost to the consumer of any article (not just gasoline).

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