In your work, you need to EXPLAIN how you got your answer to earn points Problem
ID: 3264390 • Letter: I
Question
In your work, you need to EXPLAIN how you got your answer to earn points Problems #1-#3 are ones where you are writing interpretation sentences.. In parts a and b you need to interpret your result. That means you need to write a sentence which needs to have the following components: 1) When (for what input values- include units) 2) What (what is this function/output about) 3) Increasing/Decreasing 4) By how much? Include correct units. units of a rate of change will be: "units of output per "units of input Problems #4-S6 are problems from 11.2-Marginal Analysis. Problem #1: The following graph shows U.S. verbal SAT scores as a function of the parents income level. The regression curve shown is given by (x)- -02lx+3.0x +336 (Ssxs 65) where fox) is the average SAT verbal score (in points) of a student whose parents earn x thousand dollars per year Compute the AROC over the interval 110. 201. Write a sentence to a. ccignmont cummer 2017 ndf AExplanation / Answer
Problem 1.
AROC means the average rate of change of a function.
The given function is,
f(x) = -0.021x^3 + 3.0x + 336
Now we have to find AROC over the interval [10,20]
The average rate of change of a function, f(x), over the closed interval [a, b] is given by
f(b) - f(a) / (b-a)
AROC = f(20) - f(10) / (20-10)
f(20) = -0.021*20^3 + 3.0*20+ 336 = 228
f(10) = -0.021*10^3 + 3.0*10 + 336 = 345
AROC = (228-345) / (20-10) =-11.7
Again, graphically, this is the slope of the secant line through the graph of f(x) = -0.021x^3 + 3.0x + 336
Problem 3 :
The annual demand for Justin Beiber Duck Tape can be modeled by the function.
q = 45e-0.05p
where p is the price for a roll in dollars.
Now we have to find AROC for an interval [10,15]
f(10) = 45e-0.05p = 45e-0.05*10 = 27.29
f(15) = 45e-0.05p = 45e-0.05*15 = 21.26
AROC= f(15) - f(10) / 15-10
= 21.16 - 27.29 / 5 = -1.226