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7. NOTE: This is a hard question and will be marked very strictly. Very little or no credit will be given unless you can get the final answer and your solution is completely correct. b dx Let a and b be constants such that a

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Nestor Rutherford
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23 Dec 2017
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6. A small lake is stocked with a certain species of fish. Use the simplified logistic model 4 P(t) = 1 to describe the population at time t > 0. The parameters A and k are positive constants. (b) After 4 years the population is 1500. What will the population be after 8 years? (Note that using the properties of the exponential function, you are expected to obtain an exact numerical answer, with no unevaluated exponentials or logarithms.)

8. A company is planning to produce a new electric toaster. After conducting an extensive market survey, the research department provides the following information: when the unit price is $16 per toaster, then the weekly demand is 20 toasters; for every $2 decrease in the unit price, the weekly demand increases by 10 toasters. The financial department estimate that the weekly fix costs will be $140 and the variable cost of production will be $4 per toaster. Let p be the unit price and let q be weekly demand. Note: Please simplify your answers such that your answers for (b) and (c) are given by integers. (a) Find the demand function linking p and q. Answer:

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