Chapter Practice Test
Chapter
Chapter 4
Section
Chapter Practice Test
Solutions 11 Videos

The function f(x) = - \frac{1}{2}(3^{2x + 4})+ 5 is the transformation of the function g(x) = 3^x.

a) Explain how you can tell what type of function f(x) represents by looking at the equation.

b) Create a table of values for f(x). Describe how to tell the type of function it is from its table of values.

c) Describe the transformations necessary (in the proper order) that map g(x)onto f(x) .Sketch f(x) and state the equation of its asymptote.

Q1

Evaluate. Express answers as rational numbers.

\displaystyle (-5)^{-3} 

Q2a

Evaluate. Express answers as rational numbers.

\displaystyle (27)^{\frac{2}{3}} 

Q2b

Simplify. Use only positive exponents in your final answer.

\displaystyle (-3x^2 y)^3(-3x^{-3}y)^2 

Q3a

Simplify. Use only positive exponents in your final answer.

\displaystyle \frac{(5a^{-1}b^2)^{-2}}{125a^5b^{-3}} 

Q3b

Simplify. Use only positive exponents in your final answer.

\displaystyle \sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5}} 

Q3c

Simplify. Use only positive exponents in your final answer.

\displaystyle \frac{(8x^6y^{-3})^{\frac{1}{3}}}{(2xy)^3} 

Q3d

A spotlight uses coloured gels to create the different colours of light required for a theatrical production. Each gel reduces the original intensity of the light by 3.6%.

a) Write an equation that models the intensity of light, I, as a function of the number of gels used.

b) Use your equation to determine the percent of light left if three gels are used.

c) Explain why this is an example of exponential decay.

Q4

A small country that had 2 million inhabitants in 1990 has experienced an average growth in population of 4% per year since then.

a) Write an equation that models the population, P, of this country as a function of the number of years, 72, since 1990.

b) Use your equation to determine when the population will double (assuming that the growth rate remains stable).

Q5

Which of these equations correspond to the graph? Explain how you know.

A. \displaystyle f(x) = 2(3^{-x}) + 5 

B. \displaystyle f(x) = (3^{-2x - 4}) -5 

C. \displaystyle f(x) = -0.8(3^{x - 3}) 

D. \displaystyle f(x) = -2(3^{\frac{1}{2}x - 1}) -2 

What are the restrictions on the value of n in a^{\frac{1}{n}} if a < 0? Explain.