試題詳解

12. (5%) A company grows in value by 10% each year, and also gains 20% of a growing market estimated at 100e^0.1t million dollars, where t is the number of years that the company has been in business. Therefore, the value y(t) of the company (in millions of dollars) satisfies
y' = 0.1y+20e^0.1t and y(0)= 1 (million dollars).
What is the value of this company after 5 years?
(A) 173 million dollars
(B) 167 million dollars
(C) 180 million dollars
(D) None of the above