3. Modeling: equations that represent
relationships between quantities in real life
From 1989 through 1993, the amounts (in billions of dollars) spent on
natural gas N and electricity E by United States residents can be
modeled by the follwoing equations, where t is the number of years
since 1989.
N = 1.488t2 - 3.403t + 65.59
E = -0.107t2 + 6.897t + 169.735
1.) Find a model for the total amount A (in billions of
dollars) spent on natural gas and electricity by the United
States from 1989 through 1993.
2.) According to the model, how much will be spent in 2020 on
natural gas and electricity?
3
4. Polynomials: An expression whose terms are of the form axk
where k is a nonnegative integer.
Example: 2x3 + 5x2 - 4x + 7
Degree of a polynomial: The largest exponent of a variable.
What is the degree of the example?
Monomial: A polynomial with exactly one term
Binomial: A polynomial with exactly two terms
Trinomial: A polynomial with exactly three terms
4
5. (3x2 + 2x + 1) + (2x2 + 2x + 1)
REMOVED
x
2
x x
2
x PIECES
2 2
x x x x
2
1
x 1
2 2 x x
x x 1 1
5
6. (2x2 + x - 5) + (x2 + x + 6)
REMOVED
PIECES
2 2
x x
x x 1
2 1 1
1
x 1
1 1
1
1
1 1
2 2 x x
x x 1 1
6
7. (x2 - 2x) + (x2 + 4x + 2) REMOVED
PIECES
2 x x
x 1
x
x
1
2
x
x x
2 2 x x
x x 1 1
7
8. (-2x2 + 3x - 1) + (2x - 3) REMOVED
PIECES
1
2 2 x x x
x x
1
x
x
1
1
2 2 x x
x x 1 1
8
9. (2x2 - 2x + 2) + (x2 + 2x) REMOVED
PIECES
1
2 2
x x
1
x x
2
x
x x
2 2 x x
x x 1 1
9
