The cost, C (in dollars), to produce g gallons of a chemical can be expressed as C = f(g). Using units, explain the meaning of the following statements in terms of the chemical: (a) f(200) = 1300 (b) f'(200) = 6

An economist is interested in how the price of a certain item affects its sales. At a price of $p, a quantity, q, of the item is sold. If q = f(p), explain the meaning of each of the following statements: (a) f(150) = 2000 (b) f'(150) = -25

The time for a chemical reaction, T (in minutes), is a function of the amount of catalyst present, a (in milliliters), so T = f(a). (a) If f(5) = 18, what are the units of 5? What are the units of 18? What does this statement tell us about the reaction? (b) If f'(5) = -3, what are the units of 5? What are the units of -3? What does this statement tell us?

A company's cost of producing q liters of a chemical is C(q) dollars; this quantity can be sold for R(q) dollars. Suppose C(2000)=5930 and R(2000)=7780. What is the profit at a production level of 2000?

It is difficult for climate models to predict exactly how Earth’s climate will change over the next century. Explain this difficulty in terms of (a) the complexity of the climate system. (b) human choices.

The function C(q) gives the cost in dollars to produce q barrels of olive oil. What are the units of marginal cost?

An electronics manufacturer can produce and sell x MP3 players per week. The total cost C (in dollars) of producing x MP3 players is C=93x+35,000, and the total revenue R (in dollars) is R=135x.

Find the profit P in terms of x.

The cost, $C$ (in dollars) to produce $g$ gallons of ice cream can be expressed as $C=f(g)$. Using units, explain the meaning of the following statements in terms of ice cream.

$$f(200)=350$$

The cost, C (in dollars), to produce g gallons of a chemical can be expressed as C=f(g). Using units, explain the meaning of the following statements in terms of the chemical:

$$f^{\prime}(200)=6$$

The cost function is C(q)=1000+20q. Find the marginal cost to produce the 200th unit and the average cost of producing 200 units.

The cost, $C$ (in dollars) to produce $g$ gallons of ice cream can be expressed as $C=f(g)$. Using units, explain the meaning of the following statements in terms of ice cream.

$$f^{\prime}(200)=1.4$$

The weight, W, in lbs, of a child is a function of its age, a, in years, so W=f(a). What does f'(8)=4 tell you about age and weight?

After investing $1000 at an annual interest rate of 7$B, where B=f(t). What are the units of dB/dt? What is the financial interpretation of dB/dt?

An artisan can produce and sell $x$ hats per month. The total $\operatorname{cost} C$ (in dollars) of producing $x$ hats is

$$C=460+12 x$$

and the total revenue $R$ (in dollars) is

$$R=36 x \text {. }$$

Find the profit $P$ in terms of $x$.