The annual sales y (in millions of dollars) of a company satisfy the differential equation $\frac { d y } { d t } = 0.2 ( 10 - y ) ; y ( 0 ) = 2$ . Which of the following is a verbal description of the rate of change of annual sales.

Question

Quizplus · Accepted Answer

The differential equation $\frac { d y } { d t } = 0.2 ( 10 - y )$ indicates that the rate of change of annual sales ($\frac { d y } { d t }$) is proportional to the difference between the current sales $y$ and an upper limit of $10 million. This means as sales approach $10 million, the rate of increase slows down, aligning with choice C.

The Annual Sales Y (In Millions of Dollars) of a Company