Question

A student records the internal temperature of a hot sandwich that has been left to cool on a kitchen counter, The room temperature is 90 degrees celcius. An equation that models this situation is
T (t) = 63(0.5)^t/10 +19

How much time did it take for the sandwich to reach an internal temperature of 30 degrees celcius?

Answer 1

30 = 63 (0.5) ^ t/10 + 19
then what?

Answer 2

You have to go backwards :)

Answer 3

Add 10+19 and so on

Answer 4

but its not 19 + 10 its a fraction of t/10

Answer 5

CAN U DRAW THE EQUATION OUT?

Answer 6

start by isolating the exponential part
\[0.5^t = \frac{30-19}{63}\]
Then take natural log of both sides
use log property where exponent can be brought to front
\[t \ln(0.5) = \ln(\frac{11}{63})\]
Finally solve for t
\[t = \frac{\ln(\frac{11}{63})}{\ln(0.5)}\]