Quadratic and exponential word problems: medium

A manufacturer of chemical glassware needs to purchase a certain amount of raw material. The profit,

p

, in dollars expected from purchasing

t

tons of raw material, where

t

is positive, is:

p = 50,000 (2 t - 1) (t - 5)

What is the smallest amount of raw material in tons that the manufacturer can purchase to break even with a profit of

0

dollars?

How do I enter a student-produced response on the SAT?

For student-produced response questions, solve each problem and enter your answer as described below.

If you find more than one correct answer, enter only one answer.
You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.
If your answer is a fraction that doesn’t fit in the provided space, enter the decimal equivalent.
If your answer is a decimal that doesn’t fit in the provided space, enter it by truncating or rounding at the fourth digit.
If your answer is a mixed number (such as $3 \frac{1}{2}$ ‍), enter it as an improper fraction ( $\frac{7}{2}$ ‍) or its decimal equivalent ( $3.5$ ‍).
Don’t enter symbols such as a percent sign, comma, or dollar sign.

Examples:

Answer	Acceptable ways to enter answer	Unacceptable: will NOT receive credit
$3.5$ ‍	$3.5$ ‍ , $3.50$ ‍ , $\frac{7}{2}$ ‍	$\frac{31}{2}$ ‍ , $3$ ‍ $\frac{1}{2}$ ‍
$\frac{2}{3}$ ‍	$\frac{2}{3}$ ‍ , $.6666$ ‍ , $.6667$ ‍ , $0.666$ ‍ , $0.667$ ‍	$0.66$ ‍ , $.66$ ‍ , $0.67$ ‍ , $.67$ ‍
$- \frac{1}{3}$ ‍	$- \frac{1}{3}$ ‍ , $- .3333$ ‍ , $- 0.333$ ‍	$- .33$ ‍ , $- 0.33$ ‍

Digital SAT Math