Algebra 2 Problems of the Day

Algebra 2 is not my usual subject, but I do get asked about the problems occasionally. So I've decided to run a couple of Regents problems daily for a while. If there's a positive reaction (or at least, a lack of negative reaction), I may continue it.

More Algebra 2 problems.

January 2018
5. A certain pain reliever is taken in 220 mg dosages and has a half-life of 12 hours. The function A = 220(1/2)^t/12 can be used to model this situation, where A is the amount of pain reliever in milligrams remaining in the body after t hours.
According to this function, which statement is true?

(1) Every hour, the amount of pain reliever remaining is cut in half.
(2) In 12 hours, there is no pain reliever remaining in the body.
(3) In 24 hours, there is no pain reliever remaining in the body.
(4) In 12 hours, 110 mg of pain reliever is remaining.

Answer: (4) In 12 hours, 110 mg of pain reliever is remaining.
Substitute 12 for t, and the exponent becomes (12/12), which is 1. 220 times (1/2) is 110 mg. Even without doing any math, you are told in the question that the pain reliever has a "half-life of 12 hours" -- meaning that in 12 hours, there will be half as much, which is 110.
Choice (1) is incorrect because of the fraction in the exponent. Had the exponent been simply t, then Choice (1) would have been correct. Choices (3) and (4) can be eliminated because exponential decay will not go to zero.



6. The expression (x + a)(x + b) can not be written as

(1) a(x + b) + x(x + b)
(2) x² + abx + ab
(3) x² + (a + b)x + ab
(4) x(x + a)+ b(x + a)

Answer: (2) x² + abx + ab
The coefficient for the middle term will be the sum of a and b (as in Choice (3)), not their product.
If you use the Distributive Property on choices (1), (3) and (4), you will get x² + ax + bx + ab in each case.



Comments and questions welcome.