Question

Airplane A takes off and ascends at a rate of 3000 ft/min. At the same time, Airplane B, which is flying at 30,000 ft, begins to descend at a rate of 2500 ft/min.

Let h represent the height off the ground in feet, and let t represent time in minutes.

Which system models this situation?

A. h = 3000t
h = 2500 + 30,000t

B. h = 30,000 + 3000t
h = 30,000 − 3000t

C. h = 2500t
h = 30,000 − 3000t

D. h = 3000t
h = 30,000 − 2500t

Answer 1

First thing i would ask myself,

What are the values of each Airplane's function, when the time t, is zero [t=0]
The initial condition.

Answer 2

t=0

Airplane A: h(0) = 0 ft

Airplane B: h(0) = 30,000 ft

Answer 3

Just that information will eliminate 2 of the answers

Answer 4

The rate of change of the height is constant for both planes and is the slope of the line

Answer 5

height = (slope)*t + (initial height)

Answer 6

Givens

Airplane A: h(0) = 0
m = 3000 ft/min

Airplane B: h(0) = 30,000
m = 2500 ft / min

Ascends - positive rate of change, slope
descends - negative rate of change, slope