Exponents Practice Test
Chapter
Chapter 3
Section
Exponents Practice Test
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Solutions 29 Videos

One day, 5 friends started a rumour. They agreed that they would each tell the rumour to two different friends the next day. On each day that followed, every person who just heard the rumour would tell another two people who had not heard the rumour. Find the value of A and B which will describes the relation between the number of days that have elapsed, d, and the number of people, P, who hear the rumour on that day?

P = AB^d

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Q1

Find the value of \displaystyle 4^{-\frac{1}{2}} .

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Q2

Find the equation when y = 5^x is translated 3 units down and 4 units left.

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Q3

Which is correct about exponential functions?

A. The ratio of successive first differences is constant.

B. The first differences are constant.

C. The first differences are zero.

D. The second differences are constant.

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Q4

Evaluate without use of calculator.

\displaystyle 49^{\frac{1}{2}}

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Q5a

Evaluate without use of calculator.

\displaystyle 5^{-3}

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Q5b

Evaluate without use of calculator.

\displaystyle (-4)^{0}

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Q5c

Evaluate without use of calculator.

\displaystyle (16)^{\frac{1}{4}}

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Q5d

Evaluate without use of calculator.

\displaystyle (-8)^{\frac{5}{3}}

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Q5e

Evaluate without use of calculator.

\displaystyle (\frac{3}{4})^{-4}

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Q5f

Evaluate without use of calculator.

\displaystyle (\frac{27}{64})^{- \frac{1}{3}}

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Q5g

Evaluate without use of calculator.

\displaystyle (-\frac{8}{125})^{- \frac{4}{3}}

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Q5h

Simplify. Express your answer using only positive exponents.

\displaystyle (x^{-2})(x^3)(x^{-4})

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Q6a

Simplify. Express your answer using only positive exponents.

\displaystyle \frac{p^{-3}}{p^2}

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Q6b

Simplify. Express your answer using only positive exponents.

\displaystyle (2k^4)^{-1}

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Q6c

Simplify. Express your answer using only positive exponents.

\displaystyle (a^{\frac{1}{2}})(a^{\frac{2}{3}})

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Q6d

Simplify. Express your answer using only positive exponents.

\displaystyle (y^{\frac{2}{3}})^{-6}

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Q6e

Simplify. Express your answer using only positive exponents.

\displaystyle (u^{\frac{1}{2}}v^{2})^{-2}

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Q6f

Find the equation of the given graph.

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Q8a

Find the equation of the given graph.

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Q8c

a) Sketch the graph of the function \displaystyle y = 2^{x -5} + 3

b) Identify the

  • i) domain
  • ii) range
  • iii) equation of the asymptote
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Q9

Describe the transformation(s) that map the base function y =8^x onto each function.

y = \frac{1}{3}(8^x)

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Q10a

Describe the transformation(s) that map the base function y =8^x onto each function.

y = 8^{4x}

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Q10b

Describe the transformation(s) that map the base function y =8^x onto each function.

y =-8^{-x}

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Q10c

Describe the transformation(s) that map the base function y =8^x onto each function.

y =8^{-3x-6}

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Q10d

A radioactive substance with an initial mass of 80 mg has a half-life of 2.5 days.

a) Write an equation to relate the mass remaining to time.

b) Graph the function. Describe the shape of the curve.

c) Limit the domain so that the model accurately describes the situation.

d) Find the amount remaining after

  • i) 10 days
  • ii) 15 days

e) How long will it take for the sample to decay to 5% of its initial mass?

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Q11

a) Sketch the function \displaystyle y = -\frac{1}{2} \cdot 2^{x + 3} - 1

by applying transformations to the graph of the base function y = 2^x.

b) For the transformed function, find the

  • i) domain
  • ii) range
  • iii) equation of the asymptote
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Q12

The height, h, of a square-based pyramid is related to its volume, V, and base side length, b, by the equation h = 3Vb^{-2}. A square-based pyramid has a volume of 6250 m^3 and a base side length of 25 m. Find its height.

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Q13

The population of Pebble Valley over a period of 5 years is shown.

a) Make a scatter plot for this relationship. Do the data appear to be exponential in nature? Explain your reasoning.

b) Find the equation of the curve of best fit.

c) Limit the domain of the function so that it accurately models this situation.

d) Predict the population of Pebble Valley 7 years after the first table entry. State any assumptions you must make.

e) How long will it take for the town to double in size? State any assumptions you must make.

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Q14