Saturday, April 15, 2017

Algebra 2 Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

15. The loudness of sound is measured in units called decibels (dB).
These units are measured by first assigning an intensity I0 to a very softsound that is called the threshold sound. The sound to be measured is assigned an intensity, I, and the decibel rating, d, of this sound is found using d = 10 log (I / I0).
The threshold sound audible to the average person is 1.0 X 10-12 W/m2 (watts per square meter).
Consider the following sound level classifications:

How would a sound with intensity 6.3 X 10-3 W/m2 be classified?
Moderate 45-69 dB
Loud 70-89 dB
Very Loud 90-109 dB
Defeaning > 110 dB

(3) very loud

Don't let all the logs and subscripts bother you. At the heart of this question is simple substitution and evaluation. Plug in the values and let the calculator do the rest.
The formula you are given is: d = 10 log (I / I0).
I0 = 1.0 X 10-12, and I = 6.3 X 10-3
So calculate (using enough parentheses!) the following: 10 log ( (6.3 X 10-3) / (1.0 X 10-12) )
You should get 97.99341..., which is between 90 and 109, or "Very Loud".

16. Pedro and Bobby each own an ant farm. Pedro starts with 100 ants and says his farm is growing exponentially at a rate of 15% per month. Bobby starts with 350 ants and says his farm is steadily decreasing by 5 ants per month.
Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants?

(2) 8

The equation for Pedro's farm is y = 100(1.15)x. The equation for Bobby's farm is y = 350 - 5x. (Note that Bobby is losing 5 ants, not 5%.)
Graph these on your calculator.
The two lines will intersect at a fraction past 8 months, where both will have a little less than 310 ants.
Use the CALC function (2nd and TRACE) and choose Intersection from the menu. Hit ENTER three times to get the answer.

Continue to the next problems

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