O-Level Exponential and logarithmic functions: worked solution

Question

Explain why, according to T = 30 + 175e^(-mt), the cube’s temperature can never drop below 30°C.

For any real t, e^(-mt) > 0 (an exponential is always positive), so the term 175e^(-mt) is always greater than 0. Therefore T = 30 + 175e^(-mt) is always greater than 30. As t increases, e^(-mt) decreases towards 0, so T falls towards 30 but never reaches or drops below it.