538 CHAPTER 9 Modeling Our World much does your maximum heart rate change from age 25 to age 40? What is your maximum heart rate at age 70? depreciated value of the washin time. When does the depreciate 23-28: Linear Equations. The following situations can be modeled by linear functions. In each case, write an equation for the linear func- tion and use it to answer the given question. Be sure you clearly iden- tify the independent and dependent variables. Then briefly discuss whether a linear model is reasonable for the situation described. 34. A mining company can extract with a purity of 3 ounces of go tion is $1000 per ton. If p is th ounce, find a function that giv mine as it varies with the price price of gold that makes them 23. The price of a particular model car is $18,000 today and rises with time at a constant rate of $900 per year. How much will a new car cost in 3.5 years? FURTHER APPLICATIONS 24. In 2012, Dana Vollmer set the women's world record in the 100-meter butterfly (swimming) with a time of 55.98 seconds. Assume that the record falls at a constant rate of 0.05 second 35-42: Algebraic Linear Equation. find the slope of the graph and the for values of x between -10 and 10 per year. What does the model predict for the record in 2020? 35. y = 2x + 6 25. A snowplow has a maximum speed of 40 miles per hour on a dry highway. Its maximum speed decreases by 1.l miles per hour for every inch of snow on the highway. According to this model, at what snow depth will the plow be unable to 37. у 3D —5х —5 || 39. y Зх — б 41. y = -x + 4 move? 26. The cost of leasing a car is $1000 for a down payment and processing fee plus $360 per month. For how many months can you lease a car with $3680? 43-48: Linear Graphs. The followir by linear functions. In each case, dr the graph to answer the given que: the independent and dependent v whether a linear model is reasonab 27. You can rent time on computers at the local copy center for a $10 setup charge and an additional $2 for every 5 minutes. How much time can you rent for $25? 43. A group of climbers begin cl feet and ascend at a steady r: What is their elevation after 28. In 2000, the population of Boom Town began increasing at a rate of 300 people per year. The 2000 population was 1500 people. What is your projection for the population in the 44. The diameter of a tree increa passing year. When you star diameter was 4 inches. Estir year 2020? started growing. 29-34: Equations from Two Data Points. Create the required linear function, and use it to answer the following questions. 45. The cost of publishing a pos printing equipment, plus $3 total cost to produce 2000 29. Suppose your pet dog weighed 2.5 pounds at birth and weighed 15 pounds one year later. Based on these two data points, find a linear function that describes how weight varies with age. Use this function to predict your dog's weight at 5 and 10 years of age. Comment on the validity of the model. 46. The amount of sugar in a fe with time at a rate of 0.1 gr amount of 5 grams. When 30, You can purchase a motorcycle for $6500 or lease it for a down payment of $200 and $150 per month. Find a function that describes how the cost of the lease depends on time. How long can you lease the motorcycle before you've paid more than its purchase price? 47. The cost of a particular priv one-time initiation fee of $2 How much will it cost to att 31. A Campus Republicans fundraiser offers raffle tickets for $10 each. The prize for the raffle is a $350 television set, which must be purchased with proceeds from the ticket sales. Find a function that gives the profit/loss for the raffle as it varies with the number of tickets sold. How many tickets must be 48. The maximum speed of as varies with the weight of it maintain a maximum spee tons of cargo, its maximur At what load does a linear of 0 miles per hour? CEle celos to egual the cost of the prize? 49 Wildlir