3.5. Practice question answers — Mathematics for Public and Occupational Health Professionals

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92 3.5. Practice question answers — Mathematics for Public and Occupational Health Professionals

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Chapter 3 practice question answers

1. Domain; y = years [1960,2010] ; Range, p = population, [100,1400]

2. a. Values that are less than or equal to -2, or values that are greater than or equal to -1 and less than 3

b. {x | x ≤ -2 or -1 ≤ x < 3}

c. (-∞, -2] ∪ [-1, 3)

3. Domain; y = years, [1952,2002] ; Range, p = population in millions, [40,88]

4.
<img src="https://ecampusontario.pressbooks.pub/app/uploads/sites/2699/2022/06/quicklatex.com-87e97341b2996e0889c8a34873751f95_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="T(c)=\begin{cases} 89.5c \quad if \quad c\le10\\ 895+33(c-10)\quad if \quad 1018\\ \end{cases}” title=”Rendered by QuickLaTeX.com” height=”79″ width=”715″ style=”vertical-align: -35px;”>

A reasonable domain should be whole numbers 0 to (answers may vary), e.g. [0,23]. A reasonable range should be $0 – (answers may vary), e.g. [0,1524].

5. a. {x | 2008 ≤ x ≤ 2018}, [2008, 2018]

b. {x | 16.1 ≤ x ≤ 88.4}, [16.1, 88.4]

1. $\frac{\$3.01-\$1.69}{5\;years}=\frac{\$1.32}{5\;years}=$ 0.264 dollars per year.

2. Average rate of change = $\frac{f(9)-f(1)}{9-1}=\frac{(9-2\sqrt{9})}{9-1}=\frac{(3)-(-1)}{9-1}=\frac{4}{8}=\frac{1}{2}$ .

3.
$\frac{f(a+h)-f(a)}{(a+h)-a}=\frac{((a+h)^3+2)-(a^3+2)}{h}$

4. Based on the graph, the local maximum appears to occur at (-1, 28), and the local minimum occurs at (5,-80). The function is increasing on (-∞, -1)∪(5, ∞) and decreasing on (-1, 5).

5. a. -0.59 per 100,000

b. 6

c. 2010, 2014, and 2017

1. The path passes through the origin with vertex at (-4, 7).

2. $g(x)=x^2-6x+13$ in standard form; $g(x)=(x-3)^2+4$ in vertex form.