The population of a small town in central Florida has shown a linear decline in the years 2001-2012. In 2001 the population was 22200 people. In 2012 it was 13950 people. A) Write a linear equation expressing the population of the town, P , as a function of t , the number of years since 2001. Include the entire equation as your answer.

B) If the town is still experiencing a linear decline, what will the population be in 2014?

Step-by-step explanation:

First of all, to keep our numbers manageable, we are going to let year 2001 = 0 so year 2012 = 11.  The coordinates that result from these years/population numbers are (0, 22200) and (11, 13950). Since this linear, we can plug those 2 coordinate pairs into the slope equation to find the rate at which the population is decreasing in people per year:

That means that the town is losing people at the rate of 750 per year. We can use that slop along with one of the coordinate points to write the linear equation representing this situation:

and

y = -750x + 22200. That answers part A.

Now for B we need to find y when x = 13 (remember we let year 2001 = 0, so year 2014 = 13):

y = -750(13) + 22200 so

y = 12450 people in the year 2014

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step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.