Question

A cake recipe says to bake the cake until the center is 180°F. then let the cake cool to 100°F. The table shows temperature readings for the cake.

a. Given a room temperature of 69°F, what is an
exponential model for this data set?
b. How long does it take the cake to cool to the desired
temperature?

Answer 1

8.058655822 mins

Explanation:

We have a table and to solve for this we might want to find the equation for this

This is a exponential function

To solve for this we need the rate of decay and the x intercept

We know the x intercept is 180 because in 0 mins the temp is 180

To solve for decay we need to know the temp of the cake after 1 min

to get the decay value we can do

125= 180 (x)^5

.69444444444 = x^5

0.929667185 = x

so the equation would be

180 (0.929667185)^x

if we tell this equation to equal 100

we get

100 = 180 (0.929667185)^x

.5556 = (0.929667185)^x

log .5556 = log 0.929667185 *x

log .5556 / log .929667185)

8.058655822= x

After 8.058655822 mins the cake will be 100 degrees