Newton's law of cooling is:

du/dt= -k(u-t)

where u(t) is temperature of an object, t is in hours, t is a constant ambient temperature, and k is a positive constant.

suppose a building loses heat in accordance with newton's law of cooling. suppose that the rate constant k has the value 0.15 hr ? 1 . assume that the interior temperature is ti = 70? f, when the heating system fails. if the external temperature is t = 11? f, how long will it take for the interior temperature to fall to t1 = 32? f?

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

We can reorder the expression like this:

We can use the substitution and so then we have:

IF we integrate both sides we got:

If we apply exponential in both sides we got:

And if we replace w = u-T we got:

We can also express the solution in the following terms:

For this case we know that since w ehave a cooloing, , we have this model:

And if we want that the temperature would be 32F we can solve for t like this:

If we apply natural logs on both sides we got:

So it would takes approximately 6.9 hours to reach 32 F.