A company grows in value by 10% each year, and also gains 25% of a growing...

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A company grows in value by 10% each year, and also gains 25% of a growing market estimated at 100e0.1 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 + 25e0.1t (0) = 5 (Initial value $5 million) (a) Solve this differential equation and initial condition to find a formula for the value of the company after years. y(t)= (b) Use your solution to find the value (in millions of dollars) of the company after 3 years. (Round your answer to the nearest whole number.) S million A company grows in value by 10% each year, and also gains 25% of a growing market estimated at 100e0.1 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 + 25e0.1t (0) = 5 (Initial value $5 million) (a) Solve this differential equation and initial condition to find a formula for the value of the company after years. y(t)= (b) Use your solution to find the value (in millions of dollars) of the company after 3 years. (Round your answer to the nearest whole number.) S million