MAT 128 Baltimore City Community College Vertical Profit Intercept Algebra HW

MAT 128-PRECALCULUS I: COLLEGE ALGEBRA

TEST#2 Please read the instructions and solve it. If there’s anything you need please let me know!

BCCC
MAT 128
Summer 2020
Professor: Ray Orocco-John
Student’s Name:_______________________________________________
Test #2
Show work where appropriate. Answers without adequate justification will not receive full credit.
1) (9pts) Given the following table
t
2
5
8
h
10
8
6
a) Find a formula for h(t)
11
4
b) Find the t intercept of this function
c) Find the h intercept of this function
2) (6pts) Match each graph with the corresponding line
F
B
a) y = 1.5
_______
D
b) x = 1.5
_______
c) y = x + 1
_______
d) y = 3x + 1
_______
e) y = -1 – 3x
_______
f) y = -1 – 2x
_______
C
E
A
3) (15pts) A linear function f(x) passes through the point f (−4) = −3 with a slope of ½.
a) Graph the function f(x). Be sure to label the axes.
b) Write the equation for f(x)
f(x)= ___________________
c) Write the equation of a line g(x) that is perpendicular to f(x) and passes through the point (0, 3).
g(x) = ___________________
d) Graph g(x)
e) Find the coordinates of the intersection of the lines f(x) and g(x)
4) (6pts) In 1997 we started our calculator rental program with 30 calculators and have been expanding it by
about 15 calculators each year. In what year will we exceed 400 calculators?
5) (4pts) Write the letter in the space provided that BEST describes the function over the entire domain.
i)————-The rate of change is > 0
A) An increasing linear function
ii)————The rate of change is < 0 B) A decreasing linear function iii)-----------The rate of change is undefined C) A Horizontal Line iv)-----------The rate of change is 0 D) A Vertical Line 6) (9pts) A company's profit is linearly related to the number of items the company sells. Profit is a function of the number of items sold. If the company sells 2000 items, its profit is $24,000. If the company sells 3000 items, its profit is $32,000. a) Find the slope & explain what it means in words b) Find the vertical (profit) intercept & explain what it means in words c) Find f (4380) and explain what it means in words 7) (6pts) Vivian and Noelle both leave the park at the same time, but in opposite directions. If Noelle travels 5 mph faster than Vivian and after 8 hours, they are 136 miles apart, how fast in miles per hour is each traveling? 8) (9pts) Given the function f ( x) = 3 x − 2 − 4 a. Algebraically find the coordinates of the vertical intercept b. Algebraically find the coordinates of the horizontal intercept(s) c. What are the Domain and Range of this function? 9) (2pts) Data set A has correlation of 0.8 and data set B has correlation of -0.9. Which set of data is more accurately modeled with a linear function? Why? 10) (8pts) A car rental company offers two plans for renting a car: Plan A: 30 dollars per day and 17 cents per mile Plan B: 50 dollars per day with free unlimited mileage For what range of miles will plan B save you money for a 1 day rental? In other words, to save money the mileage must be greater than how many miles per day? Give your answer accurate to at least one decimal place. 11) (8pts) Find the area of a triangle bounded by the y axis, the line f(x) = 7 − 2/3x, and the line perpendicular to f(x) that passes through the origin. 12) (6pts) Theodore needs to mix a 40% alcohol solution with a 60% alcohol solution to create 100 milliliters of a 46% solution. How many milliliters of each solution must Theodore use? 13) (12pts) In 2002, a school population was 2213. By 2009 the population had grown to 3193. a) How much did the population grow between the year 2002 and 2009? b) How long did it take the population to grow from 2213 students to 3193 students? c) What is the average population growth per year? d) What was the population in the year 2000? e) Find an equation for the population, P, of the school t years after 2000. f) Using your equation, predict the population of the school in 2013.