Chapter 4

In 1991 , the moose population in a park was measured to be 4,360 . By 1999, the population was measured again to be 5,880 . Assume the population continues to change linearly. (a) Find a formula for the moose population, \(P\) since 1990 . (b) What does your model predict the moose population to be in \(2003 ?\)

For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2 . Is each pair of lines parallel, perpendicular, or neither? Line 1: Passes through (2,3) and (4,-1) Line 2: Passes through (6,3) and (8,5)

In \(2003,\) the owl population in a park was measured to be \(340 .\) By 2007 the population was measured again to be 285 . The population changes linearly. Let the input be years since \(2003 .\) (a) Find a formula for the owl population, \(P\). Let the input be years since \(2003 .\) (b) What does your model predict the owl population to be in \(2012 ?\)

For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2 . Is each pair of lines parallel, perpendicular, or neither? Line 1: Passes through (1,7) and (5,5) Line 2: Passes through (-1,-3) and (1,1)

The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010 and is being depleted by about 2.1 billion cubic feet each year. (a) Give a linear equation for the remaining federal helium reserves, \(R,\) in terms of \(t,\) the number of years since 2010 . (b) In \(2015,\) what will the helium reserves be? (c) If the rate of depletion doesn't change, in what year will the Federal Helium Reserve be depleted?

For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2 . Is each pair of lines parallel, perpendicular, or neither? Line 1: Passes through (2,5) and (5,-1) Line 2: Passes through (-3,7) and (3,-5)

For the following exercises, write an equation for the line described. Write an equation for a line parallel to \(f(x)=-5 x-3\) and passing through the point (2,-12)

You are choosing between two different prepaid cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $$\$ 19.95$$ plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

For the following exercises, write an equation for the line described. Write an equation for a line parallel to \(g(x)=3 x-1\) and passing through the point (4,9) .

You are choosing between two different window washing companies. The first charges $$\$ 5$$ per window. The second charges a base fee of $$\$ 40$$ plus $$\$ 3$$ per window. How many windows would you need to have for the second company to be preferable?

For the following exercises, write an equation for the line described. Write an equation for a line perpendicular to \(h(t)=-2 t+4\) and passing through the point (-4,-1)

When hired at a new job selling jewelry, you are given two pay options: Option A: Base salary of $$\$ 17,000$$ a year with a commission of \(12 \%\) of your sales Option B: Base salary of $$\$ 20,000$$ a year with a commission of \(5 \%\) of your sales How much jewelry would you need to sell for option A to produce a larger income?

For the following exercises, write an equation for the line described. Write an equation for a line perpendicular to \(p(t)=3 t+4\) and passing through the point (3,1)

When hired at a new job selling electronics, you are given two pay options: Option A: Base salary of $$\$ 14,000$$ a year with a commission of \(10 \%\) of your sales Option B: Base salary of $$\$ 19,000$$ a year with a commission of \(4 \%\) of your sales How much electronics would you need to sell for option A to produce a larger income?

When hired at a new job selling electronics, you are given two pay options: Option A: Base salary of $$\$ 20,000$$ a year with a commission of \(12 \%\) of your sales Option B: Base salary of $$\$ 26,000$$ a year with a commission of \(3 \%\) of your sales How much electronics would you need to sell for option \(\mathrm{A}\) to produce a larger income?

When hired at a new job selling electronics, you are given two pay options: Option A: Base salary of $$\$ 10,000$$ a year with a commission of \(9 \%\) of your sales Option B: Base salary of $$\$ 20,000$$ a year with a commission of \(4 \%\) of your sales How much electronics would you need to sell for option \(\mathrm{A}\) to produce a larger income?

For the following exercises, sketch a line with the given features. An \(x\) -intercept of (-4,0) and \(y\) -intercept of (0,-2)

For the following exercises, sketch a line with the given features. An \(x\) -intercept (-2,0) and \(y\) -intercept of (0,4)

For the following exercises, sketch a line with the given features. A \(y\) -intercept of (0,7) and slope \(-\frac{3}{2}\)

For the following exercises, sketch a line with the given features. A \(y\) -intercept of (0,3) and slope \(\frac{2}{5}\)

For the following exercises, sketch a line with the given features. Passing through the points (-6,-2) and (6,-6)

For the following exercises, sketch a line with the given features. Passing through the points (-3,-4) and (3,0)

For the following exercises, sketch the graph of each equation. $$ f(x)=-2 x-1 $$

For the following exercises, sketch the graph of each equation. $$ f(x)=-3 x+2 $$

For the following exercises, sketch the graph of each equation. $$ f(x)=\frac{1}{3} x+2 $$

For the following exercises, sketch the graph of each equation. $$ f(x)=\frac{2}{3} x-3 $$

For the following exercises, sketch the graph of each equation. $$ f(t)=3+2 t $$

For the following exercises, sketch the graph of each equation. $$ p(t)=-2+3 t $$

For the following exercises, sketch the graph of each equation. $$ x=3 $$

For the following exercises, sketch the graph of each equation. $$ x=-2 $$

For the following exercises, sketch the graph of each equation. $$ r(x)=4 $$