Question

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 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?

Answer 1

Answer:

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: $T(t)=68e^{-0.0174t}+72$.

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.

$80=68e^{-0.0174t}+72$

Now let us solve for t.

Let us subtract 72 from both sides of our equation.

$80-72=68e^{-0.0174t}+72-72$

$8=68e^{-0.0174t}$

Let us divide both sides of our equation by 68.

$\frac{8}{68}=\frac{68e^{-0.0174t}}{68}$

$0.1176470588235294=e^{-0.0174t}$

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

$ln(0.1176470588235294)=ln(e^{-0.0174t})$

Using natural log property $ln(e^x)=x*ln(e)$ we will get,

$ln(0.1176470588235294)=-0.0174t*ln(e)$

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

$-2.1400661634962708708=-0.0174t*1$

$-2.1400661634962708708=-0.0174t$

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

$\frac{-2.1400661634962708708}{-0.0174}=\frac{-0.0174t}{-0.0174}$

$122.9923=t$

$t\approx 123$

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