Unit 2, Lesson 2
Funding the Future
Integrated Math 3
2.1
Warm-up
What do you notice? What do you wonder?
3 hundreds, 2 tens, 9 ones
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What do you notice? What do you wonder?
3 hundreds, 2 tens, 9 ones
A polynomial function of is a function given by a sum of terms, each of which is a constant times a whole number power of . The word “polynomial” is used to refer both to the function and to the expression defining it. Polynomial models are adaptable to a variety of situations even as they grow in complexity.
Let’s say we’re going to invest \$200 at an annual interest rate of . This means at the end of a year, the balance in the account is multiplied by a growth factor of . After the first year, the amount in the account can be expressed as , which is a polynomial. Similarly, after the second year, the amount will be , after three years, the amount will be , and so on.
If an additional \$350 is invested at the end of the first year, we can revise the polynomial. The amount of money in the account after 1 year is the same, but now the amount of money after two years is .
If \$400 more is invested at the end of the second year and \$150 more is invested at the end of the third year, the total value of the account can then be represented by the polynomial .
Let be the amount of money in dollars in the account after four years and be the growth factor, where . A graph of helps us visualize how the amount in the account after four years depends on different values of .
Graph of a line, origin O. Horizontal axis, x, growth factor, scale is 0 to 1 point 4 by point 2s. Vertical axis, v, dollars, scale is 0 to 2,800 by 200's. Line starts at the origin, curving upwards and to the right, passing through points A and B.
A polynomial function of is a function given by a sum of terms, each of which is a constant times a whole-number power of . The word “polynomial” is used to refer both to the function and to the expression defining it.