Given the function 8S - 14 Y(s) (s + 2) (s – 4) 1. Use Partial Fractions to break apart the large fraction into smaller fractions. 2. Then use the Laplace Transform table to convert this function into f(t).
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- From 1950 through 2005, the per capita consumption C of cigarettes by Americans (age 18 and older) can be modeled by C = 3565.0 + 60.30t − 1.783t2, 0 ≤ t ≤ 55, where t is the year, with t = 0 corresponding to 1950. In 2005, the U.S. population (age 18 and over) was 296,329,000. Of those, about 59,858,458 were smokers. What was the average annual cigarette consumption per smoker in 2005? What was the average daily cigarette consumption per smoker?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?Condition y(0) = 3 Ans. e^-4t (3+t)
- As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be N(t) = 0.00525t2 + 0.075t + 4.7 (0 ≤ t ≤ 4) million in decade t, where t = 0 corresponds to 2010.† (a)What is the projected number of people with Alzheimer's disease in the United States age 65 years and over in 2040? (Round your answer to four decimal places.) million (b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2040? million per decade (c)How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study? million per decade per decadeIt is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. Find the projected population after 24 hours for the following conditions.(a) No antibiotic is present, so the relative growth rate is 12%.(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?
- A species of butterflies is calculated to triple the size of its population every year. Which of the following represents the number of insects in x number of years if the present population is recorded in an area as 1,500? A) y=1500xy=1500x A), y is equal to 1500 x B) y=15003xy=15003x B), y is equal to 1500 raised to the 3 x power C) y=1500(3)xy=1500(3)x C), y is equal to 1500 times 3 to the x th power D) y=1500x3If the function f(t) is a solution of the initial-value problemy′ = (2t + 5)y, y(0) = 3, find f (0) and f ′(0).need asap thx (f(s) = s^2-5-12/(s-3)(s+4)(s-5)^2)
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