3) (11 PTS) A contaminated lake is treated with a bactericide. The rate of change in harmful bacteria t days after the treatment is given by N'(t) = = 14/2 , 0 S t s 10 where N(t) is the number of bacteria per millileter of water. a. (8 PTS) Find the function for the number of bacteria if the initial count was 5,000 bacteria/mL. b. (3 PTS) If the lake is safe to swim in when the number of bacteria is 100 bacteria/ml or less, will the lake be safe to swim in after 10 days? Show work to back up your answer.Lab 8 7.2-7.5, 8.1-8.3 92 1) (10 PTS) The graph shows the approximate concentration of alcohol in a person's bloodstream t hours after drinking 2 oz. of alcohol. Use Riemann Sums to estimate the total amount Alcohol concentration/hour of alcohol in the bloodstream from t = 0 to t = 8 using rectangles of width 2 hours. a. Using left-hand endpoints. Ax = Hours X2 = f( x ) = f(x2) = f (x] ) = f ( x. ) = Estimate of total amount of alcohol in the bloodstream = a. Using right-hand endpoints. Ax = * = X2 = f ( x) =. f (x2) = f (x]) = f(x. ) = Estimate of total amount of alcohol in the bloodstream = b. Now find the average of your answers in parts (a) and (b). 2) (10 PTS) A population grows at a rate of P'(x) = 500xe-*/5, where P(x) is the population after x months. a. (8 PTS) Find a formula for the population size after t months, given that the population is initially 2000. b. (2 PTS) What happens to the total population in the long run? (Hint: Find lim P(x).)4] [11 P151 A company found that its rate of prot (in thousands of dollars) after t years of operations is given by P'm = (3t + 3&2 + 2: + 2)\"? a. ['1 PTS} Find the total profit in me rst ve years. Round your FINAL answer to the nearest dollar. h. [4 PTS} Find the prot in the sixth year ofoperation. Round your FINAL answer to the nearest dollar. 5] [7 PTS} The rate of change of me voting population of a city with respect to time t {in years} is estimated to he , _ 100.! N (t) _ (la-:2? Label your answer and round to three decimal places. where N(t] is in thousands. Find like change in the voting population in the rst three years