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- How do you do Let f(x) = x2 + 2x and solve with the differential quotientIt 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%.Determine the solution of the problem with initial values
- 3 ln x + 2 ln y − 4 ln zHow do I solve the initial value problem using P(x), Q(x) and v(x)?The population of Normal, Illinois grows proportionally to its population at time t. At an initial population of 2100, it grows at a rate of 8% over 10 years. What is the value of the proportionality constant?
- 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=2A 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?For the two armies X and Y, the X army is about to attack Y army which has only 7725 troops while the X army has 12440 troops. The Y army however superior military equipment’s which make each Y soldier 1.5 times as effective as X soldier. Develop a mathematical model using differential equations and explain for i) which army will win ii) Estimate how many troops of the winning army will be left at the end. iii) How long the battle will end. The kill rates of X and Y are 0.5 and 0.75 respectively.