Question

7. The management of a bottling company estimate that their profit (in $) from the daily production and sale of x bottles is given by the equation P(x) = -0.0003 function in the window (0.150 x 10.200). How many bottles should be produced per day in order to + 9x - 420. Sketch the graph of the maximize the company's profit? What is the maximum profit? (10 pt) 8. The rate of growth of a particular type of pest can be approximated by the function: NI) - 5 + 2017 pests/month. If initially there are 20 pests present, how many will there be 8 months later? (10 pt) 9. Sketch the graph and find the area of the region under the graph of the function f(x) - 2 + V on the interval [0.8]. (10 pt) 10. The concentration of a certain drug in a patient's blood stream: hours after injection is c) - mg/cm3. Determine the total concentration of the drug in the patient's bloodstream over the first 4 hours after the drug is injected. (10 pt) 125108357083

Answer 1

Given growth rate function is N') = 6+2, +3 and initially at t=0, No2= 20 To FUTC) Ist solve differential equation N't) ié dN = 5 +20+2/3 ie Nela | Sidt f 20.4 +23.dt L. = 57 +20 x 4,513 te - 557 + 20434513 +6 Ini (t) = 5t + 12 +513 te No = 0+0+C = 20 w NCH) = 57+12+5/3 +20 so after 6 month N(3) = 5% +12 X C0143720 = 40 + 12x (213** Az = 40 +12 X 32 + 20 =o0 f384 = 444 A(8) 34.447 peste

5). Given function is - ffub c + 3 827 Home flesta ļ int! f'(u) = utazova 30 » $ ) й улсrедія Area of f(n) is given by Now trop all3) dn E Tane n938178 4 = Flo+ 3x 28.267 F16*3*643= [16492] client = 208 unit AS