Mat 117 – F21Problem Set #3

SEJ

Directions: Complete the problems on this sheet. All problems must be completed by the due date to earn full

credit. Show all work and include appropriate units where applicable. Box all final answers.

1. [4 pts] Suppose that 30 deer are introduced in a protected wilderness area. The population of the herd

𝑃 can be approximated by 𝑃(𝑥) =

30+2𝑥

1+.05𝑥

, where 𝑥 is the time in years since introducing the deer.

Write the equation of the horizontal asymptote for this function. Also, interpret what this asymptote

means in the context of the problem (in terms of the deer population and the number of years since the

deer were introduced into the wilderness area).

2. Lisa throws a horseshoe, in a game of horseshoes. The path of the horseshoe is modeled by

𝑦(𝑥) = – 0.006𝑥 2 + 0.2𝑥 + 2.5, where x represents the horizontal distance of the horseshoe from the

start and y(x) is the height of the horseshoe above the ground. (Both x and y(x) are measured in feet.)

For parts a, b, and c, round your answer(s) to 2 decimal places.

a. [3 pts] Determine 𝑦(11). Then explain what your answer means in the context of the problem. (“In

the context of the problem” means “in terms of the horseshoe’s horizontal distance from the start

and in terms of the height of the horseshoe above the ground.”)

b. [2 pts] Determine the numerical value of the vertical intercept (y intercept) and explain what this

means in the context of the problem.

c. [3 pts] Determine the numerical values of the vertex coordinates and explain what they mean in the

context of the problem.

d. [2 pts] How far from the start did the horseshoe strike the ground? (Round your answer to the

nearest whole number)

3. In Stephen King’s 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 1/2 foot. Every minute that passes, the radius

grows by 2 inches.

a. [2 pts] Create a linear function which gives the radius of the circle in inches after t minutes. Call this

function 𝑟(𝑡).

b. [2 pts] Knowing that the Area of a circle is 𝐴 = 𝜋𝑟 2 , use composition of functions to represent the

Area of the circular substance in square inches after 𝑡 minutes. Call this function 𝐴(𝑡).

c. [2 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.

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