Rate of Change of The Cost Function - Mathematics Assignment Help

Assignment Task

1. The population of a city is given by the function P (t) = 100 + where t is the time in year,

(a) (3 pts) Find the rate of change of the population, P'(t).

(b) (1 pt) Find the rate at which the population is changing when t = 3 years. Explain the meaning of your answer.

(c) (1 pt) Find the year at which the population starts to decrease. Show algebraic work.

2. The cost (in thousands of dollars) of a company is given by the function C(x) = for producing x many items.

(a) (3 pts) Find the rate of change of the cost function.

(b) (1 pt) How fast will costs be rising when 200 items are produced? Explain your answer.

3. The population of a certain type of fish at a lake after t weeks is given by P(t) = 1200e-°.°79`.

(a) (1 pt) Find P(10) and explain what it represents (interpret its meaning).

(b) (2 pts) Find P(10) and explain what it represents (interpret its meaning). 
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4. The profit, in thousands of dollars, from the sale of x thousand candles can be estimated by the function P(x) = 3x — 0.4x In x.

(a) (3 points) Find the rate of change of the profit function (this function is called marginal profit), Ps (x).

(b) (1 pt) Find P'(160) and interpret its meaning. 

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