Final answer:
A linear model relating altitude a to time t for a grain drop can be expressed as a(t) = -40t + 2000. This means the grain drops at a constant rate, losing 40 feet of altitude per second, starting from an altitude of 2000 feet and landing after 50 seconds.
Step-by-step explanation:
The student's question involves finding a linear model that relates altitude a in feet to time in the air t in seconds for a scenario where a load of grain is dropped from an altitude of 2,000 feet and lands 50 seconds later. To do this, we need two points to define the linear equation in the form of y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
At t = 0 seconds, the altitude a is 2,000 feet, which gives us our first point (0, 2000). At t = 50 seconds, the altitude is 0 feet as the grain has landed, giving us the second point (50, 0).
We can find the slope (m) by taking the change in altitude divided by the change in time:
m = (0 - 2000) / (50 - 0) = -2000 / 50 = -40
Now, we can use one of our points and the slope to find the y-intercept, which in this case is the initial altitude:
b = 2000
Therefore, our linear model is:
a(t) = -40t + 2000
This model indicates that every second, the grain loses 40 feet in altitude until it reaches the ground after 50 seconds.