10. G(t) = t5 –e-9t + 5(t – 1)2 4 16-
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10.Solve for the laplace transform using the formula.
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- The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnYAn efficiency study of the morning shift at a factory (7:00 A.M. to 12:00 noon) indicates that an average worker who arrives on the job at 7:00 A.M. will have produced Qunits t hours later, whereQ(t) = -t3 + 9t2 + 15tWhen during the morning shift does the worker’s production reach the point of diminishing returns?
- The revenue per month earned by the Couture clothing chain at timetisR(t) =N(t)S(t),whereN(t) is the number of stores andS(t) is the average revenue per store per month. Couturereleases a statement to their investors saying that currently they have 50 stores with a total revenueof$7,500,000 and expect to increase the number of stores by about 2 stores per month and increasetotal revenue by about$250,000 per month. What does this statement imply about the current rateof change of the average revenue per store per month?What is the behaviour Of the solution when t approaches to?Show (2.27) x_t - x_t-1 is stationary
- Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N= 66 x−x2. Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,589. Round to the nearest integer. $Does the function y(t) = 6e-3t satisfy the initial value problemy '(t) - 3y(t) = 0, y(0) = 6?Find f using the initial value problem
- need asap thx (f(s) = s^2-5-12/(s-3)(s+4)(s-5)^2)The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem, dN/dt=N(1-0.0005N), N(0)=1. How many supermarkets are expected to adopt the new technology when t = 10?The population of a city (in millions) at time tt (in years) is P(t)=2.7e0.002tP(t)=2.7e0.002t, where t=0t=0 is the year 2000. When will the population double from its size at t=0t=0?
