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The population of a small town in central Florida has shown a linear decline in the years 2003-2011. In 2003 the population was 41100 people. In 2011 it was 36380 people.

A) Write a linear equation expressing the population of the town, P , as a function of t , the number of years since 2003. Include the entire equation as your answer. Answer: __________________

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



Answer :

Considering the situation described, we have that:

a) The linear function is given by: y = -590x + 41100.

b) The prediction for the population in 2014 is of 34,610.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, the have that:

  • The initial population is the y-intercept of b = 41100.
  • In 8 years, the population decreased by 4720, hence the slope is of m = -4720/8 = -590.

Thus the equation is:

y = -590x + 41100.

2014 is 11 years after 2003, hence the prediction is:

y = -590(11) + 41100 = 34,610.

More can be learned about linear functions at https://brainly.com/question/24808124

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