Chapter 6B

Example: You have a new candle which is 20 cm long. For every hour it burns the length shrinks by 3 cm. Create a model. How long will the candle burn?

L: length of the candle in cm
t: time the candle has been burning in hours
slope or rate of growth/decay = -3 cm/hr
inital value = 20 cm

$L=-3t+20$

(Note that without a description of the variables with units, the equation has no meaning)

The candle will burn until the length is zero.
$0=-3t+20$
$3t=20$
$t=\frac{20}{3}$
$t=6.67$
The candle will burn for 6.67 hours or 6 hours and 40 minutes.

Problems

1. What information do you need to create a linear model?

2. You are riding a ski lift. After 5 minutes you are at 9600 feet. After 7 minutes you are at 9800 feet. Come up with a model. How high is the base of the ski lift?

3. In the spring the mountain snow melts 4 inches every 3 days. Suppose the snow begins melting on March 1st when the depth is 70 inches. Create a model. Use your model to determine how long it will take for all the snow to melt.

4. You call your long distance phone company to inquire about their domestic rates. The operator tells you that there are two calling plans. Plan A offers $0.15 per minute all the time with no monthly fee. Plan B offers $0.10 per minute all the time with a monthly fee of $4.95.
   1. Create an equation for each plan to model the cost. Make sure you label your variables.
   2. Clearly if you don't make many long distance calls, Plan A is the plan for you. What is the minimum number of minutes you would have to call each month to make plan B the better deal?

5. You want to open a hot dog stand. It will cost you $1000 to buy the cart. Each hot dog and bun with the fixin's will cost you $0.25. You sell them for $1.50.
   1. Create an equation to model the profit.
   2. Suppose you sell about 50 dogs per day. How long will it take you to break even?