Apie with a temperature of 140∘f is taken out of the oven and placed on a windowsill to cool. its temperature as a function of tminutes is given by

t(t)=68e−0.0174t+72

how long, to the closest minute, will it take for the pie to cool to
80∘f?

123 minutes.

Step-by-step explanation:

We have been given that a pie with a temperature of 140∘F is taken out of the oven and placed on a windowsill to cool. Its temperature as a function of t minutes is given by: .

To find the number of minutes it will take for the pie to cool to  80∘F, we will substitute T(t) = 80 in our given function.

Now let us solve for t.

Let us subtract 72 from both sides of our equation.

Let us divide both sides of our equation by 68.

Now let us take natural log of both sides of our equation.

Using natural log property we will get,

Since ln(e)=1 , so we will get,

Let us divide both sides of our equation by -0.0174.

Therefore, it will take approximately 123 minutes for the pie to cool to 80∘F.

72 is the answer to this problem