UMBC Math Problem Set Vertical Intercept Questions

Math Set. Problems need to be solved and work shown. Attached is the math set

MAT 117- Problem Set 3
Objectives 10-15
Directions: Complete the problems on the answer sheet provided. All problems must be completed by the end of
class to earn full credit. Show all work.
1. Quadratics.
The path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.017×2 +
1.08x + 5.8, where x represents the horizontal distance from the start and h(x) is the height of the shot put above
the ground. (Both x and h(x) are measured in feet.)
a. 4 points. Determine h(24). Round your answer to 2 decimal places. Then explain what your answer means in
the context of the problem. (“In the context of the problem” means “in terms of the shot put’s horizontal
distance from the start and in terms of the height of the shot put above the ground.”)
b. 4 points. Determine the numerical value of the vertical intercept and explain what this means in the context of
the problem.
c. 4 points. Determine the numerical values of the vertex coordinates and explain what they mean in the context
of the problem.
d. 4 points. How far from the start did the shot put strike the ground? Round your answer to 2 decimal places.
2. Singh makes a base salary of $2200 per month. Once he reaches $40000 in total sales, he earns an additional
5% commission (salary) on the amount by which his sales exceed $40000. Let s be the amount of his total sales
for the month and G(s) be the amount of his salary for the month.
a. 4 points. Graph G(s) for s values between $0 and $100000 in sales. Indicate your scale on both the horizontal
and vertical axes, and be sure to label what quantities (salary or sales) each axis represents.
3. 5 points. Suppose that 300 fish are introduced into a protected lake. The fish population can be approximated
by, 𝑃(𝑡) =
300+45𝑡
1+1.05𝑡
with t being the time in years since the fish were introduced into the lake.
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 fish population and the number of years since the fish were
introduced into the lake).