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- When Limiting Values Occur Suppose S(t) represents the average speed, in miles per hour, for a 100-mile trip that requires t hours. Explain why we expect S to have a limiting value.A tank contains 2100 L of pure water. Solution that contains 0.07 kg of sugar per liter enters the tank at the rate 9 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? (b) Find the amount of sugar after t minutes (c) Find the limit of y(t) as t approaches infinityTo create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water that initially contained 8000 L of pure water. The resulting concentration of the solution in the tank can be modelled by the function C(t)= 40t/160+t,where C is the concentration, in grams per liter, and t is the time, in minutes. a) Is there an upper limit to the concentration in the tank? Explain.b) Complete the table of reasonable values in the context of the problem. c) Graph the function in the context of the problem. Clearly label axes, asymptote, and intercept(s)
- Determine the smallest value of the constant a for which the graph of the function f(x) = ax−x is always above the x−axis. Help me fast so that I will give good rating.The cumulative sales S (in thousands of units) of a new product after it has been on the market for t years are modeled by S = 90(1 − ekt). During the first year, 4,000 units were sold. Solve for k in the model. What is the saturation point for this product? (The saturation point is the limit of S as t → ∞.) How many units will be sold after 3 years? (Round to the nearest unit.)The sales of a book publication are expected to grow according to the function S= 300000(1−e^-0.06t),where t is the time,given in days. (i) Show using differentiation that the sales never attains an exact maximum value. (ii) What is the limiting value approached by the sales function? kindly provide step by step working with explanation.
- limit as x→−∞ 4/(e^x+7)=0 Enter the left-hand asymptote: y=1. Suppose that when a patient takes a blood thinner drug at times t = 0, the amount of drug (in mg) in the patient’s blood can be modelled by:A(t) = te^(−kt)where time t ≥ 0 is measured in hours, and where k is some positive constant. (The domain of the function isD = [0, ∞).)(a) Does the function A(t) have a horizontal asymptote (for t ≥ 0)? Either compute the asymptote, or showthat there is none. Would your answer change for different values of the positive constant k?(b) Write a sentence explaining what your answer in part (a) means for the patient. Does this seem reasonable? Explain brieflyThe cumulative sales S (in thousands of units) of a new product after it has been on the market for t years are modeled by S = 90(1 − ekt). During the first year, 4,000 units were sold. Solve for k in the model. K= What is the saturation point for this product? (The saturation point is the limit of S as t → ∞.) How many units will be sold after 3 years? (Round to the nearest unit.)
- (a) The sales of a book publication are expected to grow according to the functionS = 300000(1 − e−0.06t), where t is the time, given in days. (i) Show using differentiation that the sales never attains an exact maximum value. (ii) What is the limiting value approached by the sales function? (b) A poll commissioned by a politician estimates that t days after he makes a statement denegrating women,the percentage of his constituency (those who support him at the time he made the statement) that still supports him is given by S(t) =75(t2 − 3t + 25) /t2 + 3t + 25 The election is 10 days after he made the statement. (i) If the derivative S’(t) may be thought of as an approval rate, derivate the a function for his approval rate. (ii) When was his support at its lowest level? (iii) What was his minimum support level? (iv) Was the approval rate positive or negative on the date of the election? (c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curve for…The sales of a book publication are expected to grow according to the function S=300000(1-e^-0.06t) where g is the time , given in days showing using differentiation that the sales never attains an exact maximum value. What is the limiting value approach by the sales function? A poll commissioned by a politician estimates that t after he makes a statement, denegrating women, the percentage of his constituency( those who support him at the time he made the statement) that still supports him is given by S(t)=75(t^2-3t+25)/t^2+3t+25 The election is 10 days after he made the statement if derivatives S'(t) may be thought of as an approval rate, derivate the function for his approval rate. When was his support at its lowest? What was his minimum support level? Was the approvals rate positive or negative on the date of the election(a) The sales of a book publication are expected to grow according to the functionS = 300000(1 − e−0.06t), where t is the time, given in days.(i) Show using differentiation that the sales never attains an exact maximum value.(ii) What is the limiting value approached by the sales function?(b) A poll commissioned by a politician estimates that t days after he makes a statementdenegrating women,the percentage of his constituency (those who support him at the time hemade the statement) that still supports him is given by S(t) =75(t2 − 3t + 25)/t2 + 3t + 25The election is 10 days after he made the statement.(i) If the derivative S’(t) may be thought of as an approval rate, derivate the a functionfor his approval rate.(ii) When was his support at its lowest level?(iii) What was his minimum support level?(iv) Was the approval rate positive or negative on the date of the election?(c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curvefor the bast will…