Chapter 9.B, Problem 43E

Linear Graphs. The following situations can be modeled by linear functions. In each case draw a graph of the function and use the graph to answer the given question. Be sure you clearly identify the independent and dependent variables. Then briefly discuss whether a linear model is reasonable for the situation described.

1. A group of climbers begin climbing at an elevation of 6500 feet and ascend at a steady rate of 600 vertical feet per hour. What is their elevation after 3.5 hours?
2. The diameter of a tree increases by 0.2 inch with each passing year. When you started observing the tree, us diameter was 4 inches. Estimate the time at which the tree started growing.
3. The cost of publishing a poster is $2000 for setting up the pruning equipment, plus S3 per poster pruned. What is the total cost to produce 2000 posters?
4. The amount of sugar in a fermenting hatch of beer decreases with time at a rate of 0.1 gram per day starting from an initial amount of 5 grams. When is the sugar gone?
5. The cost of a particular private school begins with a one-time initiation fee of $2000, plus annual tuition of $10,000. How much will it cost to attend this school for six years?
6. The maximum speed of a semitrailer truck up a sleep lull varies with the weight of its cargo. With no cargo, it can maintain a maximum speed of 50 miles per hour. With 20 tons of cargo, its maximum speed drops to 40 miles per hour. At what load does a linear model predict a maximum speed of 0 miles per hour?