entrepreneurial endeavor

  • 1. 27 years ago, Jurassic Park arrived in theaters. Back then, Miss Kito decided to try to capitalize off the
    success of the movie by selling novelty mosquitos trapped in amber. She called her entrepreneurial
    endeavor Miss Kito’s Mosquitos. She determined that her monthly profit in dollars was determined
    by the function = −2000
    + 12000 − 10000, where was the price per unit.
    a) [6 pts] Use the formula method to find the vertex of P(x). (Find both the x and y coordinates!)
    b) [3 pts] What should Miss Kito charge per mosquito in order to maximize her monthly profits?
    What is the maximum monthly profit? Provide your final answer using a complete sentence with
    appropriate units.
    2. [6 pts] Let = 3
    − 4 + 2

and completely simplify your answer.
3. One of Mr. Fishman’s favorite authors is Stephen King. In his short story collection “Skeleton Crew”
there is a story called “The Raft”. In this story, four college friends swim out to a raft in an isolated
lake. Upon reaching the raft they discover a circular, black substance (much like an oil slick) floating in
the water. They soon learn that the substance eats anything swimming in the lake and will not let
them leave the raft. When they first discover the circular substance, it has a radius of only 1 foot.
Every minute that passes, the radius grows by 2 inches.
a) [3 pts] Create a linear function which gives the radius of the circle in inches after t minutes. Call this
function .
b) [3 pts] Knowing that the Area of a circle is =
, use composition of functions to represent the
Area of the circular substance in square inches after t minutes. Call this function .
c) [3 pts] Use your answer to part b to find the area of the circular substance after a half hour has
passed. Round your final answer to the nearest whole number and include appropriate units.
MAT 117- Problem Set 4 Name: _______________________
Directions: Complete the problems on the answer sheet provided.
Show all work.
Submit your file as a single page PDF in Canvas.
1. (a) [3 pts] If 5
= 6, what does 5
(b) [3 pts] Solve for x in the following:


2. The Game Commission introduces 40 elk into protected state game lands. The population of
the herd is modeled by the function N t( ) where t is the number of years since the introduction into the
protected area.
10(4 2 ) ( ) 0
1 0.03
N t t

 

a. [4 pts] Find N(25) and explain what it means in the context of the problem
b. [4 pts] What is the limiting factor on the herd as time progresses? Explain your answer.
(Hint: look at asymptotes)
3. The spread of the Ebola virus in Africa in 2014 could be modeled by () = 188.59.
where represents the number of cases and represents the number of days since May 1, 2014.
(source: http://www.geert.io/exponential-growth-of-ebola.html)
a. [2 pts] Approximately how many cases were there on May 1, 2014?
b. [3 pts] How many cases were projected by June 17, 2014?
c. [4 pts] Find (23) and explain what it means in the context of the problem.

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