The record for the fastest mile run by a person has been decreasing over time. Back around 1850, when record times were first recorded, the fastest mile time recorded was about 5 minutes. By around 1950, the fastest mile time recorded was about 4 minutes.
Note: Assume that the fastest mile time (run by a person) has been decreasing linearly over time since 1850.
1. Find the function R(t) that models the (assumed) linear decrease in the fastest timed mile records over time t, where t = 0 corresponds to 1850.
2. Use your function R(t), showing all work, to predict the following:
a. The record for the fastest mile run in the year 2000
b. The year in which a mile will be run in 3 minutes
c. The year in which a mile will be run in 2 minutes
d. The year in which a mile will be run in 1 minute
e. The year in which a mile will be run in 0 minutes
3. Explain the limitations of your model.
B. An object is launched straight up into the air. Its height in feet, or h, after t seconds is given by the equation h = -16t2 + 48t + 10.
1. Determine how much time (in seconds) has elapsed from the time of launch to the time the object hits the ground.
a. Show all work.
2. Determine how much time has elapsed when the object is 30 feet above the ground.
a. Show all work.
3. Determine the maximum height reached by the projectile.
a. Show all work.
4. Determine the projectile's distance from the ground at the instant that the projectile is fired.
a. Show all work.