2:19 Sun 21 Sep ..Homework3Problem 1: Evaluate each integral. For definite integrals be sure to use the change of variables formula to create new bounds.a.01t2etdtf.dt(16-t2)22b.x(lnx)2dxe 1xx2162dxe.xsxdxb.dzz2z2-42d.0exsinxdxi.3(4x2-25)12dxe.1ex3ln(x)dxj.x2(x39)15dxProblem 2: The area covered by a patch of moss is growing at a rate ofdAdt=?2lntcm2 per day, for t1. Suppose at t=1,A(1)=0.5cm2.a. Use separation of variables to solve the initial value peoblem and state the area function A(t).b. Use the function from part (a) to evaluate the adlitional amount of area covered by the moss between 4 and 9 days.Problem 3: A computer virus nicknamed the Sapphire Worm specal throughoat the internet on Jannary 25,2003. Studies suggested that during the first few minutes, the population of inficted computer bosts increased at a rate that is proportional to the sumber of uninfected compaters consected to the internet, where the propoetionality constant is 0.0815. Further, suppose that celly 10,000 compaters were connected to the internet and at time t=0(measured in seconds),6 compater hosts were inficted answer the following questions:n. Let P(t) be the number of infected computers and write an initial value problem to represent the above scenario.b. Qualitatively explain the behavior of the family of solutions to part (a) by finding any critical points, testing before and after, and give a shorch of the solution P(t).c. Use the meparation of variables to find a solution P(t) to the inaitial value problem in part (a).d. How many compater hosts were infocted after 2 minutes? After 3 minutes?Page 1 of 2Math 141- Calculus with Analytic Geometry IIHomework 3Problem 4: When coffee is poured into a mag with no lid, its traperature is moramed at 170'F. There minutes later, its temperature is 165F. Also, the surrounding temperature at the cublee shop is set to 68'F.a. Write an initial value problem that will describe the change in the temperature of the coffee, T, as a function of time t measured in minates.b. Solve the initial value problem in part (a).c. How loag will it tale for the coffee to cool off to 25F?1 of 2