402 CHAPTER 6 Algebra, Graphs, and Functions 74. Golf Ball Height Eldrick is at Top Golf, and he hits a golf ball off the top of a building. The height of the ball, h t( ), above the ground, in feet, can be determined using the quadratic function, = − + + h t t t ( ) 16 80 54, 2 where t is the time, in seconds, after the ball is hit. a) What is the height of the ball when it is hit? 54 feet b) What is the height of the ball after 2 seconds? 150 feet c) What is the height of the ball after 5 seconds? 54 feet 75. Lakewood Ranch Hourly Temperature The following graph was created using StatCrunch with data obtained from AccuWeather.com. The graph indicates the hourly temperature, in degrees Fahrenheit, in Lakewood Ranch, Florida, from 10 a.m. to 6 p.m. on March 17, 2023. The quadratic function t x x x ( ) 0.65 5.16 64.42 2 = − + + can be used to estimate the hourly temperature, where x is the number of hours since 10 a.m. and ≤ ≤ x 0 8. Temperature(8F) 80 Hourly Temperature in Lakewood Ranch, Florida, on March 17, 2023 60 40 20 0 Time 6 10 11 1 2 3 4 5 12 Source: AccuWeather.com a) Use the function t x( ) to estimate the temperature in Lakewood Ranch at 1 p.m. Round your answer to the nearest degree. 74°F b) Use the graph to determine the hour that the temperature was a maximum. 2 p.m. c) Determine the x-coordinate of the vertex of the graph of t x( ). Then use this value in t x( ) to estimate the maximum temperature. Round your value of x to the nearest hour. Round your answer for the temperature to the nearest degree. 4 hours or 2 p.m.; 75°F 76. Dubuque Hourly Temperature The following graph was created using StatCrunch with data obtained from AccuWeather.com. The graph indicates the hourly temperature, in degrees Fahrenheit, in Dubuque, Iowa, from 9 a.m. to 5 p.m. on March 17, 2023. The quadratic function t x x x ( ) 0.59 4.71 44.39 2 = − + + can be used to estimate the hourly temperature, where x is the number of hours since 9 a.m. and ≤ ≤ x 0 8. Temperature(8F) 60 Hourly Temperature in Dubuque, Iowa, on March 17, 2023 30 10 20 0 Time 5 50 40 9 10 1 2 3 4 11 12 Source: AccuWeather.com a) Use the function t x( ) to estimate the temperature in Dubuque at 12 p.m. Round your answer to the nearest degree. 53°F b) Use the graph to determine the hour that the temperature was a maximum. 1 p.m. c) Determine the x-coordinate of the vertex of the graph of t x( ). Then use this value in t x( ) to estimate the maximum temperature. Round your value of x to the nearest hour. Round your answer for the temperature to the nearest degree. 4 hours or 1 p.m.; 54°F 77. Population of Mexico The population of Mexico in 2021 was about 126.7 million people. Assume that the population of Mexico continues to grow exponentially at the growth rate of about 0.6% per year. The expected population of Mexico, P t( ), in millions of people, t years after 2021, can be estimated by the exponential function = ( ) 126.7(1.006) . P t t Use this function to estimate the population of Mexico in the year 2031. Source: Census.gov 134.51 million 78. Population of Canada The population of Canada in 2021 was about 38.3 million people. Assume that the population of Canada continues to grow exponentially at the growth rate of about 0.5% per year. The expected population of Canada, P t( ), in millions of people, t years after 2021, can be estimated by the exponential function = ( ) 38.3(1.005) . P t t Use this function to estimate the population of Canada in the year 2031. Source: Census.gov 40.26 million 79. Adjusting for Inflation If P is the price of an item today, the price of the same item n years from today, P ,n is = + P P r (1 ) , n n where r is the constant rate of inflation. Determine the price of a movie ticket 10 years from today if the price today is $12.00 and the annual rate of inflation is constant at 3% $16.13 80. Value of a Car The cost of a new car is $30,000. If it depreciates at a rate of 18% per year, the value of the car in t years can be approximated by the function = V t( ) 30,000(0.82) . t Determine the value of the car in 4 years. $13,563.65 $ $
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