Classwork 1: Prerequisites
Calculus I, MTH 231, Fall 2016
Instructor: Abhijit Champanerkar
Date: Aug 29, 2016 Topic: Functions
Name:
1. Bright toaster company found that the manufacturing cost C is linear in terms of the
number of toasters t. It costs $1050 to manufacture 10 toasters and $1350 to manufacture
30 toasters. Find the equation of C in terms of t. What is the cost of manufacturing
200 toasters ?
2. You want to fence off a rectangular garden adjacent to a barn (with no fence along the
barn). Find the area of the largest garden possible with 80 feet of fencing.
3. Match the equations with their graphs.
(a) 2x − 3y = 6 Graph:
(e) 4x − 3y = 8 Graph:
(b) 2y + 3x = 0 Graph:
(f) 2x + 3y = 6 Graph:
(c) y = x2 + 3x − 2 Graph:
(g) y = x2 − 3x − 3 Graph:
(d) y = 5 − x2 Graph:
(h) y = 5x − x2 − 4 Graph:
1
2
3
6
6
6
4
4
4
2
2
2
0
0
0
-2
-2
-2
-4
-4
-4
-6
-6
-6
-4
-2
0
2
4
6
-6
-6
-4
-2
4
0
2
4
6
-6
6
6
4
4
4
2
2
2
0
0
0
-2
-2
-2
-4
-4
-4
-6
-6
-4
-2
0
2
4
6
-4
-2
0
2
4
6
2
4
6
8
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-4
-2
0
2
4
6
0
2
4
6
2
4
6
-6
-6
7
-6
-2
6
6
-6
-4
5
-6
-4
-2
2
0
-6
-4
-2
0
4. A culture contains 20,000 bacteria initially. After two hours the bacteria count is 55,000.
Assuming exponential growth, how long will it take the bacteria population to reach
100,000.
5. Fill in the table using exact values.
θ
0
π/6
π/4
sin θ
cos θ
tan θ
3
π/3
π/2
6. Match the functions with their graphs.
(a) y = tan(2t) Graph:
(e) y = tan(3t) Graph:
(b) y = sin(3t) Graph:
(f) y = 8e−t/10 cos(5t) Graph:
(c) y = 8e−t/10 cos(5t) Graph:
(g) y = −3 cos(2t) Graph:
(d) y = −2 cos(3t) Graph:
(h) y = sin(3t) Graph:
1
2
3
4
5
6
7
8
9
4