An algae bloom in a lake is a sudden growth of algae that consumes nutrients and blocks sunlight, killing other life in the water. Suppose that the number of tons y(t) of algae after t weeks satisfies the following.

y' = ty + t

y(0) = 2

(a) Solve this differential equation and initial condition.

y(t)=

(b) Use your solution to find the amount of algae after 2 weeks. (Round your answer to the nearest ton.)

_____________tons

(c) Graph the solution on a graphing calculator and find when the algae bloom will reach 40 tons. (Round your answer to one decimal place.)

______________week