\fA population of algae in a small pond grows as the organisms reproduce. The population of algae after t hours is modelled by the equation P(t) = 150e24. a) What is the initial population of algae (t=0)? b) At what rate is the population changing after 30 mins? c) When was the population of algae increasing at a rate of 600 organisms per hour? Answer to the nearest minute.The net monthly profit, in dollars, from the sale of a certain item is given by the formula P(x) - 60 ze 0.35 + 10 where x21 is the number of items sold, in hundreds. If the factory can produce up to 1000 items per month, determine the number of items that yield the maximum profit. What is this maximum profit?Differentiate the following functions. a) y= b) f(x) (47 ) (57 )Differentiate the following functions. a) f(x) = sin(3x + 2) b) f(x) = ex cos(x)