Daily Regents: Exponential Functions and Inequalities

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

June 2014, Questions 26 and 27

These two half-page questions are short and easy to explain, so we'll do both of them today.

26. The breakdown of a sample of a chemical compound is represented by the function p(t) = 300(0.5)^t, where p(t) represents the number of milligrams of the substance and t represents the time, in years. In the function p(t), explain what 0.5 and 300 represent.

This is a definition question. There is no solving involved, but you do you have answer referencing the question.

The 300 represents the original amount of the chemical compound.
The 0.5 represents the rate of decay of the compound.

27. Given 2x + ax - 7 > -12, determine the largest integer value of a when x = -1.

Substitute -1 for x:

2(-1) + (-1)a - 7 > -12 Combine like terms: -a - 9 > -12 Add 9 to both sides: -a > -3 Multiply by -1 and don't forget to flip the inequality symbol: a < 3

The largest integer value less than 3 is 2.

Any questions?

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If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.