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Solutions
47 Videos

Evaluate.

a) `11^0`

b) `(-4)^0`

c) `(\dfrac{2x}{7})^0`

d) `-2^0`

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Q2

a) Identify each function as linear, quadratic, or neither. Justify your choice.

i) `f(x) = 7^x`

ii) `f(x) = 3x + \sqrt 6`

iii) `f(x) = 1 - x^2`

b) Without calculating the finite differences, describe the relationship between the finite differences and each type of function.

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Q3

Write each as a power with a positive exponent.

a) `x^{-3}`

b) `3b^{-2}`

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Q4

Write each as a power with a negative exponent.

a) `\dfrac{1}{w^4}`

b) `\dfrac{-3}{b^8}`

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Q5

Evaluate.

`6^{-3}`

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Q6a

Evaluate.

`5^{-2} + 5^{-3}`

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Q6b

Evaluate.

`(12^{-4})(12^3)`

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Q6c

Evaluate.

`\dfrac{(8^3)(8^{-4})}{8^{-2}}`

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Q6d

Evaluate.

`(\dfrac{6}{5})^{-3}`

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Q6e

Evaluate.

`(-\dfrac{8}{7})^{-2}`

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Q6f

Simplify. Express your answers using only positive exponents.

`(3b^{-5})^{-2}`

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Q7a

Simplify. Express your answers using only positive exponents.

`(-2a^2b^{-2})^{-3}`

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Q7b

Simplify. Express your answers using only positive exponents.

`(3x^4)^9 \div (3^5x^6)^3`

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Q7c

Simplify. Express your answers using only positive exponents.

`(\dfrac{2c^4}{3d^2})^{-5}`

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Q7d

Simplify. Express your answers using only positive exponents.

`(\dfrac{6^3a^5}{5^5b^9})^7 \times (\dfrac{5^{11}b^2}{6^6a^3})^3`

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Q7e

Evaluate.

`(-\dfrac{27}{64})^{-\frac{2}{3}}`

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Q8a

Evaluate.

`(-\dfrac{27}{64})^{-\frac{2}{3}}`

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Q8a

Evaluate.

`(\dfrac{16}{81})^{-\frac{7}{4}}`

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Q8b

Evaluate.

`27^{\frac{1}{3}} + 16^{\frac{3}{4}} - 32^{\frac{4}{5}}`

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Q8c

Evaluate.

`^5\sqrt{243^2}`

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Q8d

Express each radical as a power with a rational exponent.

`(^5\sqrt{-3125})^4`

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Q9a

Express each radical as a power with a rational exponent.

`(^5\sqrt{32})^3`

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Q9b

Express each power as a radical. Then evaluate.

`(-32)^{\frac{4}{5}}`

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Q10a

Express each power as a radical. Then evaluate.

`343^{-\frac{2}{3}}`

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Q10b

Express each power as a radical. Then evaluate.

`(-125)^{\frac{2}{3}}`

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Q10c

Express as a single power and then evaluate.

`16^{\frac{5}{4}} \times 16^{\frac{1}{2}} \div 16^{\frac{9}{4}}`

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Q11a

Express as a single power and then evaluate.

`81^{\frac{1}{2}} \div 81^{\frac{3}{4}} \times 81^{\frac{7}{4}}`

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Q11b

Express as a single power and then evaluate.

`256^{\frac{1}{4}} \times 256^{\frac{3}{8}} \div 256^{\frac{1}{2}}`

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Q11c

Simplify. Express your answers using only positive exponents.

`\dfrac{s^{\frac{3}{4}}}{s^{\frac{1}{3}}}`

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Q12a

Simplify. Express your answers using only positive exponents.

`(m^{\frac{3}{7}}n^{\frac{4}{5}})^{\frac{2}{3}}`

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Q12b

Simplify. Express your answers using only positive exponents.

`(k^{\frac{3}{7}})^{-\frac{1}{2}}`

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Q12c

Simplify. Express your answers using only positive exponents.

`6v^{\frac{1}{2}}(32v^{-\frac{1}{3}})^{-\frac{6}{5}}`

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Q12d

The area, A, of an equilateral triangle with side length s is given by `A = \dfrac{\sqrt 3}{4s^{-2}}`

.

Rearrange the formula to express the side length sin terms of the area A.

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Q13a

The area, A, of an equilateral triangle with side length s is given by `A = \dfrac{\sqrt 3}{4s^{-2}}`

.

Use your answer in part a) to determine the length of the sides when the area is `12.6 m^2`

.

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Q13b

Graph each function and identify the

i) domain

ii) range

iii) x- and y-intercepts, if they exist

iv) intervals of increase/decrease

v) asymptote

`f(x) = (\dfrac{1}{6})^x`

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Q14a

Graph each function and identify the

i) domain

ii) range

iii) x- and y-intercepts, if they exist

iv) intervals of increase/decrease

v) asymptote

`y = 4 \times 3.5^x`

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Q14b

Graph each function and identify the

i) domain

ii) range

iii) x- and y-intercepts, if they exist

iv) intervals of increase/decrease

v) asymptote

`y = -(\dfrac{1}{4})^x`

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Q14c

A radioactive sample, with an initial mass of 28 mg, has a half-life of 5 days.

a) Write an equation to represent the amount, A, of radioactive sample that remains after t days.

b) Explain why this situation represents exponential decay.

c) Without graphing, describe the shape of the graph of this function. State the domain and range.

d) What is the amount of radioactive sample remaining after 2 weeks?

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Q15

Sketch a graph of `y = 4^{-1.5x + 3}`

, by using `y = 4^x`

as the base and applying transformations.

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Q16

a) Describe the transformations that must be applied to the graph of `f(x) = 0.5^x`

to obtain the transformed function `$y = 2f[\dfrac{1}{3}(x - 5)]. The write the corresponding equation.

b) State the domain, range, and equation of the horizontal asymptote.

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Q17

a) Write the equation of the function that represents `f(x) = (\dfrac{1}{4})^x`

after it is compressed horizontally by a factor of `\dfrac{1}{2}`

, compressed vertically by a factor of `\dfrac{1}{3}`

, reflected in the x-axis, and shifted 4 units to the left and 6 units up.

b) State the domain, range, and equation of the horizontal asymptote.

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Q18

The population of Canada in 1981 was approximately 24 million. The population since then has increased approximately 1.4% per year.

Make a table of values by determining the population every 2 years for 20 years, since 1981.

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Q19a

The population of Canada in 1981 was approximately 24 million. The population since then has increased approximately 1.4% per year.

Determine an equation that models the data in part a).

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Q19b

The population of Canada in 1981 was approximately 24 million. The population since then has increased approximately 1.4% per year.

What was the population of Canada in 2000? Round your answer to the nearest hundred thousand.

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Q19c

Predict the population in 2012, to the nearest hundred thousand.

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Q19d

According to the model, when will Canada's population reach 40 million?

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Q19e

A bacteria colony that has an initial population of 85 triples every hour.

a) Which function models this exponential growth?

A `p(n) = 85 \times 3^n`

B `p(n) = 85 \times 2^n`

C `p(n) = 85 \times 3^n`

b) For the correct model, explain what each part of the equation means.

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Q1