Exam 1: Linear Functions and Change

The following figure shows the graph of $y=f(x)$ . Estimate $\Delta f(x) / \Delta x$ between $x=$ 5 and $x=10$ .

Which of the following graphs is mostly likely to represent the resale price of a car which depreciates steadily until it is worthless?

Let $f(t)$ be the number of students (in thousands) attending MNO college $t$ years after 2000. Which of the following statements gives the meaning of the expression $f(15)=13$ ?

The following table shows the height of a tree (to the nearest foot) as a function of time (in years). What was the average rate of change in the height of the tree between $t=6$ and $t=8$ ?

The following table shows the relationship between $s$ , the side length of an equilateral triangle, $p$ , the perimeter of the triangle, and $A$ , the area of the triangle. If $p$ is a linear function of $\mathrm{s}$ , give its rate of change. If it is not linear, enter "not linear".

You have $\$ 90$ to spend on lunches this month. Each day, you can pack a lunch for about $\$ 1.75$ , or you can buy lunch at the cafeteria for $\$ 5.25$ . Let $p$ be the number of times you pack a lunch and $b$ be the number of times you buy lunch. The formula for $p$ in terms of $b$ is given by $p=$ _____ - _____ $b$ . Round answers to 2 decimal places.

Several years ago, the wild rabbits of Australia were seriously threatened by a virus that was accidentally released into their population. Suppose that the following table gives the number $r$ of rabbits (in millions) remaining $t$ months after the release of the virus. Use a calculator program to find the linear regression line for this data and use this to estimate how many million rabbits were left after 19 months. Round to the nearest whole number.

At a price of $\$ 2.80$ per gallon, the average weekly demand by consumers for gasoline is 43 gallons. If the price rises to $\$ 2.85$ , the weekly demand drops to 39 gallons. Assuming demand is linear, let $Q=b+m p$ , where $Q$ is the weekly quantity of gasoline demanded and $p$ is the price per gallon. Then $b=―――$ and $m=―――$

Determine the point of intersection of the linear functions

Find a formula for the linear function that has $\mathrm{x}$ -intercept -3 and $\mathrm{y}$ -intercept 9 . Express your answer in $y=m x+b$ form.

Let $y=p(x)$ be defined by the following graph. If $p(x)=\mathrm{g}$ , what is $x$ ? If there is more than one answer, enter the smallest first and separate them by semicolons.

The population of a pack of rats can be represented by the formula $P(t)=3+1.3 t$ where $P(t)=3+1.3 t$ represents the population in hundreds, and $t$ represents the time, in months, since January 2010. Which of the following is correct regarding the vertical intercept?

Find the value of the expression $x^{2}-3 x y$ if $x=3$ and $y=\frac{1}{5}$ .

A study was done that collected data on 100 individuals' grade point averages and the number of hours per week they spent working. A linear regression was done on this data and the corresponding correlation coefficient was 0.3. What does this tell you about the relationship between grade point averages and working?

Farmer Brown starts with 120 cows and the average rate of change of his herd is 9 cows per year. Farmer Jones starts his herd the same year with 170 cows and the average rate of change of his herd is 5 cows per year. a) After 10 years, which farmer has the most cows? b) After 20 years, which farmer has the most cows?

Are the lines $y=-0.5 x+4$ and $y=-0.5 x-1$ parallel, perpendicular, or neither?

If $A=65+2.2 t$ and $B=25+4.2 t$ represent the population (in millions) of two countries, $A$ and $B$ , then in what year will the population of country $A$ double the population of country $B$ ? Round to 2 decimal places.

Are the lines represented by these equations parallel? Perpendicular? Or neither?

The following table gives the number of people $P$ living in a town $t$ years after 1990 . Use a calculator program to find the linear regression line for this data.