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You are going on a road trip and want to rent a car. You need to decide which agency to rent a car from. Agency A charges \$50 plus 10 cents (0.10 dollars) for each mile you drive. Agency B charges \$30 plus \$0.20 per mile. Agency C charges \$0.50 for each mile you drive. The cost in dollars for renting a car for one day from these three different rental agencies and driving it $d$ miles is given by the following equations:
$A=50+0.10d$ $B=30+0.20d$ $C=0.50d$
Graphs of the cost equation for each of the three agencies are shown on the grid to the left.
A company that manufactures and sells running shoes has a fixed overhead cost of \$65000 — that is, they need to spend \$65000 to start making shoes, no matter how many they make. It costs the company an additional \$20 to produce each pair of running shoes and it sells each pair of shoes for \$70.
Slide the values of $a$ and $b$ so that the equations for $C=65000+an$ and $R=bn$ match the equations you found in findShoeEqs. Click or tap inside the grid and drag or use the left and right arrow keys to answer the following questions.
The amount of money a company makes (its revenue minus its cost) is called its profit.
Slide the values of $a$, $b$, and $c$ so that the equations $P=a+bt$ and $G=ct$ match the equations you found in findPhoneEqs.
The tables below show the world birth and death rates per 1000 people for the years 1990-2015. The data from these tables is plotted on the grid to the left.
There are two lines which you will move to try to find a good “fit” to the data from the tables. Look to the right of the grid. The numbers 3.047 and 1.733 after the $~$s are called the root-mean-square errors of the lines. The root-mean-square error tells you how far away a line is from the data (a smaller number means the line is a better “fit” to the data).
On the grid to the left, the equations $B=mt+n$ (for the birth rate) and $D=pt+q$ (for the death rate) are graphed. Alternate sliding the values of $m$ and $n$, as well as $p$ and $q$, until you find approximately the best equation for each set of data. Your root-mean-square error should be less than 0.7 for $B$ and less than 0.1 for $D$. (On the vertical axis you see the rate of birth and death per 1000 people. On the horizontal axis you see the number of years since 1990.)