# C3 Differentiation - Exponential Growth and Decay - Quick QuestionWatch

#1
Hey

I'm doing a past paper, and the questions is:

"A heated metall ball is dropped into a liquid. As the ball cools, its temperature, T, t minutes after it enters the liquid is given by:

T = 400e^-0.05t + 25, t > 0.

Explain why the temperature of the ball can never fall to 20c.

Can anyone walk me through the reasoning behind the answer?
0
7 years ago
#2
(Original post by EnVogue)
Hey

I'm doing a past paper, and the questions is:

"A heated metall ball is dropped into a liquid. As the ball cools, its temperature, T, t minutes after it enters the liquid is given by:

T = 400e^-0.05t + 25, t > 0.

Explain why the temperature of the ball can never fall to 20c.

Can anyone walk me through the reasoning behind the answer?
For all values of t, e^-0.05t >0 (and as t gets very big, e^-0.05t approaches 0)

so T is always greater than 25 so T never falls to 20
0
7 years ago
#3
e^x can never be less than 0 (for real numbers), so as t->infinity e^-0.05t -> 0

So your minimum value will be:

T= 0+25 (well slightly more as e^-0.05t wont quite reach 0)
0
7 years ago
#4
(Original post by EnVogue)
Hey

I'm doing a past paper, and the questions is:

"A heated metall ball is dropped into a liquid. As the ball cools, its temperature, T, t minutes after it enters the liquid is given by:

T = 400e^-0.05t + 25, t > 0.

Explain why the temperature of the ball can never fall to 20c.

Can anyone walk me through the reasoning behind the answer?
0
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