The temperatures of two objects are modeled (in °C) by and

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

The temperatures of two objects are modeled (in °C) by

T_1(t)=60e^{-0.02t}+20

and

T_2(t)=40e^{-0.05t}+20

, where

t

is in minutes. Find the time at which the two temperatures are equal and state which object cools faster immediately after that instant.