Question

A cake is removed from an oven. The temperature, in degrees Fahrenheit, of the cake after t minutes can be modeled by the equation, f(x)=70+140e^-0.024t.

What is the temperature of the cake at the moment it is removed from the oven and about how long will it take for the cake to reach a temperature of 80oF ? Round your answer to the nearest whole minute.

Thank you (:

Answer 1

210°F

110 minutes

Explanation:

Given that :

Temperature of cake t minutes after being removed from oven :

f(x)=70+140e^-0.024t

Temperature T the timee it is removed ;

At this point, the time t = 0

f(t)=70+140e^-0.024t

f(x)=70+140e^-0.024(0)

= 70 + 140(1)

= 210°F

how long will it take for the cake to reach a temperature of 80oF

80 = 70+140e^-0.024t

80 - 70 = 140*e^-0.024t

10/140 = e^-0.024t

0.0714285 = e^-0.024t

In(0.0714285) = - 0.024t

−2.639057 = - 0.024t

t = 2.639057 / 0.024

t = 109.9607

t = 110 minutes