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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?Find linearly independent functions that are annihilated by the given differential operator. (Give as many functions as possible. Use x as the independent variable. Enter your answers as a comma-separated list.) (D-4)(3D + 4) Need Help? Read ItThe differential operator D4 annihilates the functions
- Imagine that we can quarantine infected members of the population, so that they are unable to transmit the disease to others. Let q represent the fraction of the infected population which is quarantined, and let 1-q represent the fraction of the infected population that is not quarantined and can transmit the disease to the susceptible individuals. (Please use google sheets) a. Rewrite the difference equation for S[t+1] and I[t+1] (from question 1), to incorporate the effects of quarantine. (Hint: quarantine should affect the term representing the proportion of susceptible individuals who are interacting with infected each time step) b. In the model you developed for question 1 implement the fraction of quarantined people by adding (1-q) to the equations for S and I. Show what happens for a quarantine percentage of 50%, meaning that 50% of infectious people are in quarantine and cannot interact with the susceptible. What can you tell about the impact of quarantine.The revenue R (in millions of dollars) for a company from 1999 to 2005 can be modeled by the equation below, where t is the year, witht = 9 corresponding to 1999. R = 0.59221t4 – 18.0042t3 + 175.293t2 - 316.42t – 116.5 Polo Ralph Lauren Revenue R 4000 3500 3000 2500 2000 1500 9 10 1I 12 13 14 15 Year (9 + 1999) (a) Find the slope of the graph for the year 2002. (Round your answer to two decimal places.) Find the slope of the graph for the year 2004. (Round your answer to two decimal places.) (b) What are the units for the slope of the graph? O dollars per year millions of dollars millions of dollars per year dollars no units Interpret the slope of the graph in the context of the problem. The slope of the graph at time t is the rate at which sales are increasing. The slope of the graph at time t is the rate at which average sales are increasing. The slope of the graph at time t is the total amount of sales. The slope of the graph at time t is the effect time has had on sales. O The…i need help with d as mentioned i need explantion why
- A linear function is such that ?(3) = 8 and ?(−2) = 2. Find the formula for the linear function.Beth makes a deposit into an account which credits interest at a nominal interest rate of 9% per annum, convertible semiannually. At the same time, David deposits 1000 into a different bank account, which is credited with simple interest. At the end of 4 years, the forces of interest on the two accounts are equal, and David's account has accumulated to X. Find the value of X. X =Use total differentials to solve the following exercise. An electronics company's profit in dollars from making x DVD players and y Blu-ray players per day is given by the following profit function P(x, y). If the company currently produces 290 DVD players and 320 Blu-ray players, estimate the extra profit that would result from producing three more DVD players and six more Blu-ray players. P(x, y) = 2x2 - 3xy + 3y2
- Estimate f(−1.99,−1.03) given that f(−2,−1)=−3, fx(−2,−1)=4, and fy(−2,−1)=1.Let f(x,y)=2x+7xy, find f(0,−3), f(−3,2), and f(3,2).The windchill index announced during the winter by the weather bureau measures how cold it "feels" for a given temperature t (in degrees Fahrenheit) and wind speed w (in miles per hour). It is calculated by the formula C(t, w) = 35.74 + 0.6215t - 35.75w 0.16 + 0.4275tw0.16 + '.+ If the temperature is 31 degrees and the wind speed is 10 miles per hour, estimate the change in the windchill temperature if the wind speed increases by 4 miles per hour and the temperature drops by 5 degrees. (Round your answer to two decimal places.)