The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by q=-2p+320, where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? What is the largest monthly revenue?

As the human population continues to grow, how do you think it will affect the use of natural resources?

Suppose that in the indicated examples fixed costs are increased to $20,000. Find the total-cost, total-revenue, and total-profit functions.

Economic profit is defined as:
a. total revenue minus implicit costs
b. total revenue plus explicit costs
c. total revenue plus implicit costs
d. wages plus interest minus rent
e. total revenue minus implicit and explicit costs

Derive the following laws for complex numbers from the corresponding laws for real numbers.

$$z_1+z_2=z_2+z_1\text{, }z_1z_2=z_2z_1\text{ (Commutative laws)} (z_1+z_2)+z_3=z_1+(z_2+z_3),\text{ (Associative laws)}(z_1z_2)z_3=z_1(z_2z_3)\text { }(z_1)(z_2+z_3)=z_1z_2+z_1z_3\text { (distributive law)} 0+z=z+0=z, \text{ }z+(-z)=(-z)+z=0\text{, }z*1=z$$

The cost of renting tuxes for the Choral Society’s formal is $20 down, plus$88 per tux. Express the cost C as a function of x, the number of tuxedos rented. Use your function to answer the following questions. a. What is the cost of renting 2 tuxes? b. What is the cost of the 2nd tux? c. What is the cost of the 4,098th tux? d. What is the variable cost? What is the marginal cost? e. Graph C as a function of x.

An exponential model of the form y = ab$^{x}$ can be rewritten as a natural exponential model of the form ________.

A bacterial culture starts with $500$ bacteria and doubles in size every half hour. How many bacteria are there after $3$ hours?

Use a graphing utility to graph the logarithmic function. Find the domain, vertical asymptote, and x-intercept of the logarithmic function. $f(x)=\log _{3}(x-4)$

For each demand equation, express the total revenue R as a function of the price p per item, sketch the graph of the resulting function, and determine the price p that maximizes total revenue in each case. q=−4p+100

In 2005, the Las Vegas monorail charged $3 per ride and had an average ridership of about 28,000 per day. In December, 2005 the Las Vegas Monorail Company raised the fare to$5 per ride, and average ridership in 2006 plunged to around 19,000 per day. a. Use the given information to find a linear demand equation. b. Give the units of measurement and interpretation of the slope. c. What would be the effect on ridership of raising the fare to $6 per ride?

In 2005, the Las Vegas monorail charged $3 per ride and had an average ridership of about 28,000 per day. In December 2005 the Las Vegas Monorail Company raised the fare to$5 per ride, and average ridership in 2006 plunged to around 19,000 per day. a. Use the given information to find a linear demand equation. b. Find the price the company should have charged to maximize revenue from ridership. What is the corresponding daily revenue? c. The Las Vegas Monorail Company would have needed $44.9 million in revenues from ridership to break even in 2006. Would it have been possible to break even in 2006 by charging a suitable price?

Suppose A and B are two events such that P(A) = 0.3, P(B) = 0.4, and $P(A \cap B)=0.12.$ Are events A and B independent? Justify your answer.

A bacterial culture starts with 500 bacteria and doubles in size every half hour. How many bacteria are there after t hours?