Applied exercises: Linear functions

At an altitude of 5000 m above Gloomington, dark clouds come up and it starts to rain. The raindrops fall down 500 m in one minute.

(Image source: https://pixnio.com/de/landschaften/regen/regentropfen-wasser#)

(a) Calculate the height of the raindrops above the ground after one, two and five minutes. Create a table of values from this.

(b) Find a function that gives the altitude $f(x)$ of the raindrops in m as a function of the elapsed time $x$ in minutes. (For simplicity, you can assume that there is no ground and the raindrops continue falling after reaching an altitude of 0m.)

(c) Visualize the relationship from (b) by a plot.

(d) How long does it take for the raindrops to reach the ground?