In 1820, let C(n) be a citys cost, in millions of dollars, for plowing the roads, when n

A cup of coffee at 90C is put into a 20C room when t = 0. The coffees temperature is changing at a rate of r(t) = 7(0.9t) C per minute, with t in minutes. Estimate the coffees temperature when t = 10.

If the marginal cost function C(q) is measured in dollars per ton, and q gives the quantity in tons, what are the units of measurement for =900 800 C(q) dq? What does this integral represent?

The marginal cost of drilling an oil well depends on the depth at which you are drilling; drilling becomes more expensive, per meter, as you dig deeper into the earth. The fixed costs are 1,000,000 riyals (the riyal is the unit of currency of Saudi Arabia), and, if x is the depth in meters, the marginal costs are C(x) = 4000+10x riyals/meter. Find the total cost of drilling a 500-meter well.

The population of Tokyo grew at the rate shown in Figure 5.65. Estimate the change in population between 1970 and 1990. 1990 0.5 P(t) t (years) rate of growth (million/year) 1970 Figure 5.65

A marginal cost function C(q) is given in Figure 5.66. If the fixed costs are $10,000, estimate: (a) The total cost to produce 30 units. (b) The additional cost if the company increases production from 30 units to 40 units. (c) The value of C(25). Interpret your answer in terms of costs of production. 10 20 30 40 50 60 0 10 20 30 40 50 C(q) q (quantity) $/unit Figure 5.66

Figure 5.67 shows the rate of change of the quantity of water in a water tower, in liters per day, during the month of April. If the tower had 12,000 liters of water in it on April 1, estimate the quantity of water in the tower on April 30. 6 12 18 24 30 100 50 0 50 100 150 t (days) rate (liters/day) Figure 5.67

The total cost in dollars to produce q units of a product is C(q). Fixed costs are $20,000. Themarginal cost is C(q) = 0.005q2 q + 56. (a) On a graph of C(q), illustrate graphically the total variable cost of producing 150 units. (b) Estimate C(150), the total cost to produce 150 units. (c) Find the value of C(150) and interpret your answer in terms of costs of production. (d) Use parts (b) and (c) to estimate C(151).

The marginal cost C(q) (in dollars per unit) of producing q units is given in the following table. (a) If fixed cost is $10,000, estimate the total cost of producing 400 units. (b) How much would the total cost increase if production were increased one unit, to 401 units? q 0 100 200 300 400 500 600 C(q) 25 20 18 22 28 35 45

The marginal cost function for a company is given by C(q) = q2 16q + 70 dollars/unit, where q is the quantity produced. If C(0) = 500, find the total cost of producing 20 units. What is the fixed cost and what is the total variable cost for this quantity?

The marginal cost function of producing q mountain bikes is C(q) = 600 0.3q + 5 . (a) If the fixed cost in producing the bicycles is $2000, find the total cost to produce 30 bicycles. (b) If the bikes are sold for $200 each, what is the profit (or loss) on the first 30 bicycles? (c) Find the marginal profit on the 31st bicycle.

The marginal revenue function on sales of q units of a product is R(q) = 200 12q dollars per unit. (a) Graph R(q). (b) Estimate the total revenue if sales are 100 units. (c) What is the marginal revenue at 100 units? Use this value and your answer to part (b) to estimate the total revenue if sales are 101 units.

Figure 5.68 shows P(t), the rate of change of the price of stock in a certain company at time t. (a) At what time during this five-week period was the stock at its highest value? At its lowest value? (b) If P(t) represents the price of the stock, arrange the following quantities in increasing order: P(0), P(1), P(2), P(3), P(4), P(5). 5 P(t) t (weeks) $/share per week Figure 5.68

The net worth, f(t), of a company is growing at a rate of f(t) = 2000 12t2 dollars per year, where t is in years since 2005. How is the net worth of the company expected to change between 2005 and 2015? If the company is worth $40,000 in 2005, what is it worth in 2015?

The graph of a derivative f(x) is shown in Figure 5.69. Fill in the table of values for f(x) given that f(0) = 2. x 0 1 2 3 4 5 6 f(x) 2 1 2 3 4 5 6 1 1 x f(x) Figure 5.69: Graph of f, not f

The derivative f(x) is graphed in Figure 5.70. Fill in the table of values for f(x) given that f(0) = 10. x 0 1 2 3 4 5 6 f(x) 10 1 2 3 4 5 6 4 4 8 x f(x) Figure 5.70: Graph of f, not f

What does the value of =t0 0 r(t) dt tells us about the oil well?

Rank in order from least to greatest: < 2t0 0 r(t) dt, < 2t0 t0 r(t) dt, < 3t0 2t0 r(t) dt.

In Problems 1820, let C(n) be a citys cost, in millions of dollars, for plowing the roads, when n inches of snow have fallen. Let c(n) = C(n). Evaluate the expressions and interpret your answers in terms of the cost of plowing snow, given c(n) < 0, < 15 0 c(n) dn = 7.5, c(15) = 0.7, c(24) = 0.4, C(15) = 8, C(24) = 13.< 24 15 c(n) dn

In Problems 1820, let C(n) be a citys cost, in millions of dollars, for plowing the roads, when n inches of snow have fallen. Let c(n) = C(n). Evaluate the expressions and interpret your answers in terms of the cost of plowing snow, given c(n) < 0, < 15 0 c(n) dn = 7.5, c(15) = 0.7, c(24) = 0.4, C(15) = 8, C(24) = 13.C(0)

In Problems 1820, let C(n) be a citys cost, in millions of dollars, for plowing the roads, when n inches of snow have fallen. Let c(n) = C(n). Evaluate the expressions and interpret your answers in terms of the cost of plowing snow, given c(n) < 0, < 15 0 c(n) dn = 7.5, c(15) = 0.7, c(24) = 0.4, C(15) = 8, C(24) = 13.c(15) + < 24 15 c(n) dn

Which is larger: < 2 0 r(t) dt or < 4 2 r(t) dt?

Which is larger: < 4 0 r(t) dt or 4r(4)?

Give a reasonable overestimate of < 8 0 r(t) dt.