A plane was flying at an altitude of 30,000 feet when it began the descent toward the airport. The airplane descends at a rate of 850 feet per minute.
a. What is the function rule that describes this situation?
b. What is the altitude of the plane after it has descended for 8 minutes? Show
your work.
c. Usethefunctioninpartatodeterminehowlongittakesfortheplaneto
land if it descends at a continuous rate.
Prentice Hall Algebra 1 • Teaching Resources
a) new altitude x = 30,000 - 850.t
b) x = 30,000 - 850.8
x = 30,000 - 6,800
x = 23,200 ft
c) x = 30,000 - 850.t
new altitude is 0 ft :
850.t = 30,000
t = 30,000 / 850
t = 35.29 min
a. To find the function rule that describes this situation, we can use the given information that the airplane descends at a rate of 850 feet per minute. Let's use "h" to represent the altitude in feet and "t" to represent the time in minutes. The initial altitude is 30,000 feet, and the descent rate is -850 feet per minute (negative because it's descending). Therefore, the function rule that describes this situation is:
h(t) = 30,000 - 850t
b. To find the altitude of the plane after it has descended for 8 minutes, we can substitute t = 8 into the function we found in part a:
h(8) = 30,000 - 850(8)
= 30,000 - 6,800
= 23,200
The altitude of the plane after 8 minutes of descent is 23,200 feet.
c. To find how long it takes for the plane to land, we can set h(t) = 0 (since the plane will reach the ground when the altitude is 0) and solve for t:
0 = 30,000 - 850t
850t = 30,000
t = 30,000 / 850
t ≈ 35.29
Therefore, it will take approximately 35.29 minutes for the plane to land if it descends at a continuous rate.
a. The function rule that describes this situation is:
Altitude = Initial altitude - Rate of descent * Time
b. To find the altitude of the plane after it has descended for 8 minutes, we can use the function rule:
Altitude = 30,000 - 850 * 8
Altitude = 30,000 - 6,800
Altitude = 23,200 feet
So, the altitude of the plane after descending for 8 minutes is 23,200 feet.
c. To determine how long it takes for the plane to land, we need to find the time when the altitude reaches 0.
Using the function rule, we set the altitude to 0 and solve for time:
0 = 30,000 - 850 * time
Simplifying the equation:
850 * time = 30,000
Dividing both sides by 850:
time = 30,000 / 850
time ≈ 35.29 minutes
So, it takes approximately 35.29 minutes for the plane to land if it descends at a continuous rate.