-1
$\begingroup$

Been asked a question and i can't seem to put it all together, i cant tell if there's not enough information or if i'm just being dumb.

A cup of hot milk cools from 100 degrees C cools to room temperature (2.8 degrees C). After ten minutes the temperature of the milk is 30 degrees C. Modeling this cooling process using an exponential function of the form. $$f(t) = Ae^{-kt}+B ,$$ determine an appropriate value for the constant $A$ to 2 decimal places.

There's the question, any help will be greatly appreciated.

$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

HINTS

So let $f(t) = Ae^{-kt} + B$ denote the temperature of the milk at time $t \ge 0$.

  • What should $f(0)$ be? Can you express $f(0)$ in terms of $A,B,k$? What constraint do you get?
  • What is the long-term (i.e. after a very long time) temperature of the milk? What constraint can you derive from here?
  • You have a point on the curve, since after 10 minutes, the temperature is $30^\circ$, can you derive a constraint from here?

You now have 3 constraints on 3 variables, can you solve the system for $A$?

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .