(a) Find a function f(x) for the total amount of money Jessa earns by charging $x per copy.

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3 1. Jessa is deciding how much to charge for her self-published memoir. The number of copies she sells is a linear function of the amount that she charges. If she charges $10 per copy, she ll sell 200 copies. If she charges $30 per copy, she ll sell 140 copies. (a) Find a function f(x) for the total amount of money Jessa earns by charging $x per copy. (b) How much should she charge in order to maximize her revenue?

4 2. You have 900 meters of fencing to build an enclosure next to a long building, so fencing is not needed along the building side. The enclosure will have a partition (made of the same fencing material) perpendicular to the building, as illustratedbelow. building (a) What should the dimensions (length and width) of the enclosure be to maximize the area of the enclosure? (b) What is the maximum possible area of the enclosure?

5 1. You have 1000 meters of fencing with which to build two enclosures. One will be a circle, and the other will be a square. The circular enclosure will also have a partition which is the length of the circle s diameter. For example, your enclosures might look like this: (a) What should the radius of the circle be to minimize the combined area of the circle and square? (b) What should the radius of the circle be to maximize the combined area of the circle and square?

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8 5. People are moving out of Beattle (mostly because it s filled with bees). (a) [4 points] The population was 500,000 in 2010, and every year it decreases by 3.7%. Write a function f(t) for the population of Beattle, t years after (b) [6 points] Meanwhile, the number of bees in Beattle is growing exponentially! In the year 2014, there was one bee for every person in Beattle. In the year 2025, there will be three bees for every person in Beattle. Write a function g(t) for the number of bees in Beattle, t years after (c) [5 points] When will there be five million bees in Beattle? Round your answer to the nearest year.

9 4. (14 points) The human population of the city of Boom is growing exponentially. Let x be the years since 2000 and B(x) be the human population in Boom. In 2000 (x=0), the human population of Boom was The human population of Boom doubles every 5 years. (a) Give the value of x when the population of Boom will be 15,000. (b) As more people inhabit the city, the population of deer within the city limits is decreasing according to an exponential model. In 2003 (x=3), the population of deer was In 2006, the population of deer was For what value of x will there be twice as many people as deer.

10 1. There were monkeys on Island X in In 1945, there were monkeys on the island. In 1935, there were half as many parrots as monkeys on the island. The number of parrots doubles every 22 years. Assuming the population of monkeys grows exponentially, when will there be three times as many parrots as monkeys? Give your answer in years after 1930.

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14 1. (15 pts) Consider the function ( ). a) (7 pts) Compute the inverse function, ( ). Show all steps. Indicate the correct domain for the inverse function. b) (8 pts) In this part, there is no need to show work or justify your answers. Start with the basic function ( ), restricted to domain. List the graph shifts, stretches or compressions, and reflections which, when applied to the graph of ( ) in the listed order, would result in the graph of ( ). Be precise (ex: first a shift up by 2 units ). Horizontally: First Then Vertically: First Then If we start with domain for ( ), what is the resulting domain after the above transformations?

15 1. Let f(x) = x,andg(x) =2x + x 2. The function h(x) =g(f(x)) is one-to-one. Find h 1 (x).

16 2. (a) Suppose f(x) = p x +2x, and g(x) =e x +3. Compute f(g(x)). (b) Suppose f(x) = p x +2x. Compute its inverse function, f 1 (x). (c) Suppose f(x) = p x +2x. Give the rule for h(x), whose graph is that of f(x) after being dilated vertically by a scaling factor of 2, and then translated down 3 units.

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18 4. f(x) is a linear-to-linear rational function such that the curve y = f(x) passes through the points (1, 9) and (10, 60) and has vertical asymptote x =7. (a) [9 points] Write a formula for f(x). (b) [6 points] Write a formula for its inverse function, f 1 (x).

19 1. The height of Rita s favorite tree is a linear-to-linear rational function of time. Today, it is 8feettall.Fiveyearsfromtoday,itwillbe12feettall.Twenty years from today it will be 16 feet tall. When will the tree be 18 feet tall? Express your answer is years fromtoday.