Each year a certain amount of money is deposited in an account that pays an annual interest rate of , so that at the end of each year the balance in the account is multiplied by a growth factor of . $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 .
2. What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%?

Consider the polynomial function given by . Evaluate the function at .

An open-top box is formed by cutting identical squares out of the corners of a rectangular piece of paper and then folding up the sides. The volume in cubic inches of this type of open-top box is a function of the side length , in inches, of the square cutouts and can be given by . What are the dimensions of the rectangular piece of paper?

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 , in square meters, of the playground space is a function of the length , in meters, of each of the sides perpendicular to the wall of the daycare building.

1. What is the area of the playground when ?
2. Write an expression for .
3. What is a reasonable domain for in this context?

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

Coordinate plane, x, negative 1 to 6 by 1, y, negative 40 to 60 by 10. Curve starts near negative point 5 comma negative 40, increases to approximately 1 point 5 comma 52, decreases through 3 point 5 comma 0 to 5 comma negative 30, then increases through 6 comma 0 to 7 comma 65.

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

Consider the expression .

1. Is the expression equivalent to ? Explain your reasoning.
2. Is the expression in standard form? Explain your reasoning.