After a certain car is turned on, the engine block heats up according to the differential equation $\frac{d H}{d t}=-K(H-100)$ for K, a positive constant.Suppose that the engine block was 20° C when the car was started, and it was 90° after running for 15 minutes.Find K to 3 decimal places.

Question

Quizplus · Accepted Answer

The Answer of After a certain car is turned on, the engine block heats up according to the differential equation $\frac{d H}{d t}=-K(H-100)$ for K, a positive constant.Suppose that the engine block was 20° C when the car was started, and it was 90° after running for 15 minutes.Find K to 3 decimal places.

After a Certain Car Is Turned On, the Engine Block dHdt=−K(H−100)\frac{d H}{d t}=-K(H-100)dtdH​=−K(H−100)

After a Certain Car Is Turned On, the Engine Block $\frac{d H}{d t}=-K(H-100)$