word problem with composite functions
Hey guys. I need help with this question. I solved b) c) and d) through simple problem-solving, but im not sure how to do a)
The temperature of the Earth's crust is a linear function of the depth below the surface. An equation expressing the relationship is T = 0.01d + 20, with the temperature (T) in Celsius and the depth (d) in metres.
a) If you were to go down the shaft of an elevator in a mine at a rate of 5 m/s, express the temperature as a function of the time travelled in the elevator in seconds.
b)Use this composite to find the temperature after the following amounts of time in the elevator. i) 5 seconds ii) 10 seconds
I know you travel 5m per second, so 5*5 = 25s and 10*5= 50s. According to the formula, i know the temperature will increase 1 degree for every 100m travelled, so after 5 seconds, the temperature will be 20.25 degrees. After 10 seconds, the temperature will be 20.5 degrees.
c) How long would it take to reach a temperature of 25°C?
25 degrees = 5 degrees above 20 degrees. 5 * 100 seconds (temperture will increase 1 degree every 100 seconds) = 500 seconds
d) At what depth would this happen?
100 seconds * 5 meters per second = 500 meters