# Lesson 2

Funding the Future

### Problem 1

Select all polynomial expressions that are equivalent to $$6x^4+4x^3-7x^2+5x+8$$.

A:

$$16x^{10}$$

B:

$$6x^5+4x^4-7x^3+5x^2+8x$$

C:

$$6x^4+4x^3-7x^2+5x+8$$

D:

$$8+5x+7x^2-4x^3+6x^4$$

E:

$$8+5x-7x^2+4x^3+6x^4$$

### Solution

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### Problem 2

Each year a certain amount of money is deposited in an account which pays an annual interest rate of $$r$$ so that at the end of each year the balance in the account is multiplied by a growth factor of $$x=1+r$$. $500 is deposited at the start of the first year, an additional$200 is deposited at the start of the next year, and \$600 at the start of the following year.

1. Write an expression for the value of the account at the end of three years in terms of the growth factor $$x$$.
2. What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%?

### Solution

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### Problem 3

Consider the polynomial function $$p$$ given by $$p(x)=5x^3+8x^2-3x+1$$. Evaluate the function at $$x=\text-2$$.

### Solution

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### Problem 4

An open-top box is formed by cutting squares out of a 5 inch by 7 inch piece of paper and then folding up the sides. The volume $$V(x)$$ in cubic inches of this type of open-top box is a function of the side length $$x$$ in inches of the square cutouts and can be given by $$V(x)=(7-2x)(5-2x)(x)$$. Rewrite this equation by expanding the polynomial.

### Solution

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### Problem 5

A rectangular playground space is to be fenced in using the wall of a daycare building for one side and 200 meters of fencing for the other three sides. The area $$A(x)$$ in square meters of the playground space is a function of the length $$x$$ in meters of each of the sides perpendicular to the wall of the daycare building.

1. What is the area of the playground when $$x=50$$?
2. Write an expression for $$A(x)$$.
3. What is a reasonable domain for $$A$$ in this context?

### Solution

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(From Unit 2, Lesson 1.)

### Problem 6

Tyler finds an expression for $$V(x)$$ that gives the volume of an open-top box in cubic inches in terms of the length $$x$$ in inches of the square cutouts used to make it. This is the graph Tyler gets if he allows $$x$$ to take on any value between -1 and 7.

1. What would be a more appropriate domain for Tyler to use instead?
2. What is the approximate maximum volume for his box?

### Solution

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(From Unit 2, Lesson 1.)