Question

2. At tine t O minutes a patient is admimisteread a drug. The drug is absorbed in the body at the rate of e- for all times t s 0. Use a Riemann sum with 2 subintervals and right end points to estimate the amount of the 3. You are measuring the ability of an antibiotic to kill harmful bacteria. You measure the rate at which the antibiotic kills bacteria (i.e., number of bacteria killed in one hour); this is called the mortality rate. You measure the following data for the number of bacteria killed in a 12 hour time period starting at t 0, and ending at t 12 Time, t Mortality rate, per hour m(t) 20 300 350 400 500 450 410 350 320 300 200 100 110 Estimate the number of deaths between t0 and t 12. 6 10 12 4. A car is driving on a straight track. Assume that the direction the car is facing is the positive direction. The graph of the velocity, v, of a car measured in ft/sec is shown below. 4 3 12 1.4 16 1 02 0.4 0.6 08 -3 -4 (a) Estimate how far does the car travels in the first second and in which direction it traveled (b) Assuming the car started at an initial position of s(0) 10ft, what is the position of the car at time t 1.3 seconds 5. Find the areas described below. (a) The area bounded by y 2 and y- 2x. (b) The area between sin 2x and cos x from x = 0 to x-π/2. (c) The area of the triangle with corners at (0,0), (1,5) and (5,1). 6. At time t = 0 it is determined that there are 100 gallons of pollution in a lake and more pollution is entering the lake at a rate (in gallons per hour) given by the formula f(t) = 10 (1-e-0.59. where t is the time (in hours). At the same time, a pollution filter begins to remove the pollution at a rate of g(t) 0.4t as long as pollution remains in the lake. (a) What is the change in the amount of pollution present in the lake between t-1 and t-4? (b) How much pollution is in the lake after 12 hours?

Answer 1

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