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- 1. Find the moment generating function of the following,Consider the following real-world problem: Suppose that the population of Memphis is 22,400, and 60% of the population are susceptible to contract a serious illness from a very contagious bacteria that was introduced as a form of biological warfare. The remaining people have no reaction to the bacteria. Assume the susceptible people are equally mixed throughout the population. On January 1, 2022 (time t=0), the number N(t) of people who had contracted the disease was 180 and was increasing at the rate of 39 per day. Assume that N’(t) is proportional to the product of the numbers of those who have caught the disease and of those who have not. Write the differential equation that models the physical situation and solve for the exact answer.(a) = -x +1 (b) = y? – 1 (c) = -y+1 (d) 22 – y? %3D (e) = x – 1 (f) 2 = y +1 (g) de -y? +1 (h) de -2² + y? de 2 H 2 y of -1 -1 -2 -2 -2 -1 i 2 -2 -1 i 2 2 2 1 1 У о Y of -1 -1 -2 -2 -2 -1 i 2 -2 -1 ở 1 Enter the letter of the DE for each of the four slopefields: ||
- The annual sales of Crimson Pharmacy are expected to be given by S = 2.2 + 0.5t million dollars t years from now, whereas the annual sales of Cambridge Pharmacy are expected to be given by S = 1.3 + 0.7t million dollars t years from now. When will Cambridge's annual sales first surpass Crimson's annual sales?The purchasing power (real value of money) decreases if inflation is present in the economy. For example, the purchasing power of $39,000 after t years of 5% inflation is given by the model P=39,000e−0.05t dollars. How long will it take for the value of a $39,000 pension to have a purchasing power of $19,500 under 5% inflation?5z - 2y 18 17. 2x – 3y = 1 5x - 7y = 4 %3D of ranahions