Question

Liquid going through a cooling system is chilled so that its temperature decreases at a constant rate from 100 degrees Celsius to 25 degrees Celsius in 5 seconds. Which of the following functions represents the temperature C, in degrees Celsius, as a function of the time t, in seconds, after chilling began, for 0 is less than or equal to t, which is less than or equal to 5? PLZ EXPLAIN

A. C equals negative 25 plus 15 t
B. C equals 25 minus 15 t
C. C equals 25 plus 15 t
D. C equals 100 minus 15 t

Answer 1

D. C equals 100 minus 15 t

Since it drops 100-25 over 5 seconds, we assume uniformly, then 75/5 = 15°/sec

C = 100 - 15t

Answer 2

A typical linear equation has the following (point-slope) form
y=mx+b
where
y=result (dependent variable), temperature in this case
x=the value of the variable, time in this case We use t instead of x for the variable name
m=slope, i.e. how much y varies when x increases by a unit (1).
b=initial value, i.e. value of y when x (or t) = 0.

Therefore, in the given case,
initial value = 100 degrees

Question says temperature decreases uniformly from 100 to 25 degrees in 5 seconds, i.e. it DROPPED 75 degrees in 5 seconds, or it was 75/5=15 degrees LESS per second, so m=-15.

So we have just found the equation to describe the temperature with respect to time,
y=mt+b
=(-15)t+100

Said in words, we say temperature C = 100 minus 15t.