An a my baker is making a cake for a Terran visitor. The cake is removed from the over at 357 and cools to 130 after 25 min in a room at 72. How long will it take for the cake to cook off to 90?

It will take 43.37 mins for the cake to cook off to 90

Step-by-step explanation:

From Newton's law of cooling

Where

time

= Temperature of the given body at time

= Surrounding temperature

= Initial temperature of the body

and = constant

From the question,

= 357

= 72

= 357 - 72 = 285

∴

From the question, the cake cools to 130 after 25 min. Then, we can write that

∴

Then,

Take the natural log (ln) of both sides

∴

Now, to determine how long it take for the cake to cook off to 90

That is,

Take the natural log (ln) of both sides

∴

Hence, it will take 43.37 mins for the cake to cook off to 90.