Question

The temperature in Gavin's oven is a sinusoidal function of time. Gavin sets his oven so that it has a maximum temperature of 320°F and a minimum temperature of 260°. Once the temperature hits 320°, it takes 20 minutes before it is 320° again. Gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 310°. He puts the cake into the oven when it is at 290° and rising. How long will Gavin need to leave the cake in the oven? (Round your answer to the nearest minute.)

Answer 1

The sinusoidal function could be written as

T = 290 + 30*sin[pi*t/(10 min)].

When does T first get to 300,

after the cake is put in? It happens when

1/3 = sin[pi*t / (10 min)]

0.339837 = pi*t / (10 min)

1.0817 minutes = t

This means the oven will stay above 300F for

2*(5 - 1.0817) minutes in each cycle

= 10 - 2.1634 = 7.8366 minutes.

He must leave it in the oven for 3 full cycles;

during the 4th cycle he can remove it after

1.0817 + (30 - 3*7.8366)

= 7.572 minutes.

Answer: 68 minutes