Unit 2, Lesson 2

Funding the Future

Algebra 2

2.1

Warm-up

Notice and Wonder: Writing Numbers

What do you notice? What do you wonder?

<p>Image. 3 grids of 100 squares, 2 grids of 10 squares, 9 single squares.</p>

3 hundreds, 2 tens, 9 ones

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2.2

Activity

Polynomials and Integers

Consider the function given by .

Evaluate the function at and .
How does knowing that help you solve the equation ?

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2.3

Activity

A Yearly Gift

At the end of 8th grade, Clare’s aunt started investing money for her to use after graduating from high school four years later. The first deposit was $300. If is the annual interest rate of the account, then at the end of each school year the balance in the account is multiplied by a growth factor of .

After one year, the total value is . After two years, the total value is . Write an expression for the total value after graduation in terms of .
If Clare’s aunt had invested another $500 at the end of her freshman year, what would the expression be for the total value after graduation in terms of ?
Suppose that $250 was invested at the end of sophomore year, and $400 at the end of junior year in addition to the original $300 and the $500 invested at the end of freshman year. Write an expression for the total value after graduation in terms of .
is the total amount in the account, in dollars, after four years, given a growth factor of . If the total Clare receives after graduation is , use a graph to find the interest rate that the account earned.

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Student Lesson Summary

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 .

Glossary

polynomial

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.

Practice

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Funding the Future

Warm-up

Notice and Wonder: Writing Numbers

Are You Ready for More?

Activity

Polynomials and Integers

Are You Ready for More?

Activity

A Yearly Gift

Are You Ready for More?

Student Lesson Summary

Glossary

polynomial