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In Problems 19–26, sketch the graph of each function. Be sure to label three points on the graph
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- Suppose that a political campaign by Loki estimates that the candidate’s polling percentage yand the amount x (in hundred thousands of pesos) that is spent on television advertising arerelated by y = e^0.3x + (5lnx)^2 while the amount that is spent on social media advertising are related by (x −3)^4 + 3y = x. (a) If P300,000 has been spent on television advertising by Loki’s campaign, determine therate of spending that will increase his polling percentage by 2 percentage points per week. (b) Suppose that Loki’s political adversary, Thor, is slowly ramping up his presence on socialmedia. If Loki’s team plans on spending P400,000 on social media advertising and the rateof spending is at P100,000 per week, at what rate will the polling percentage increase?Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1) where x=0 corresponds to year 1990. A) How many pounds of Aluminum were shipped in 2004 B) Assuming the continued accuracy of the model when will aluminum shipments reach 247,400,000,000 pounds.Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x + 1) where x=0 corresponds to year 1990 a) How many pounds of aluminum were sipped in 2004? b) Assuming the continued accuracy of the model, when will aluminum shipments reach 27,400,000,000 pounds?
- Suppose that Evelyn’s utility function is given as: U(x,y) = xyEvelyn has an income of Php 100. For simplicity purposes, the prices of both goods are equal to one. Suppose that because of President Beybiem’s failed policy to control prices, the price of good x increases to Php 2.00. To do damage control of the failed policy, the Department of Social Welfare and Social work was tasked to calculate how much should the people, including Evelyn, be compensated. (Hint: Use Evelyn’s expenditure function E(p,U).It 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%.Suppose a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.
- Suppose we have a revenue function given by R(x)=3x^3−αx, where α is a constant. What would the value of α need to be to have an average revenue of $10 when x=5?When it comes to bacteria growing by binary fission, its generation time will be the time interval required for the cells to divide. The formula for generation time would be G=t/3.3log(b/B). G would represent the generation time t represents the time interval in hours, minutes b represents the number of bacteria at the end of a time interval B is the number of bacteria at the beginning of the time interval a) What would be the generation time of the bacteria population that increases from 103 - 106 cells of 5 hours of growth b)If the growth interval was 4 hours and the generation time was for 18 minutes; what would be the increase in the bacteria population?The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given byƒ(t) = 500e0.1t,under certain storage conditions, where t is time in days after packing of the product and the value of ƒ(t) is in millions. (a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?(b) If t = 0 corresponds to January 1, what date should be placed on the product?
- A manufacturing company has been experimenting with a new additive that is used to reduce polluting effluents from its production facility. Test results suggest that if no additive is used, pollution levels are 3000 parts per million (ppm). For each pound of additive used per week, pollution levels are reduced by 0.49 ppm. The additive costs $30 per pound. The reason for experimenting with the additive is that a government agency is conducting weekly air quality tests in the vicinity of the production facility. Regulations state that if pollution levels exceed 2000 ppm, a fine is imposed. The fine is $1000 for each ppm by which the pollution level exceeds the 2000 ppm limit. If the company has budgeted $80,000 per week to spend on the additive and any pollution fines, how much additive should be purchased each week for use by the company? What is the resulting amount that the company is willing to pay in terms of weekly fines?Then what would the value of x be if g(x) is less than or equal to 0 and also how do you find the net change in g between x=1 and x=2The 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?