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The population of a small town in central Florida has shown a linear decline in the years 2005-2016. In 2005 the population was 47900 people. In 2016 it was 43500 people.

A) Write a linear equation expressing the population of the town, P , as a function of t , the number of years since 2005. Include the entire equation as your answer. Answer: ______________

B) If the town is still experiencing a linear decline, what will the population be in 2018?



Answer :

Considering the situation described, we have that:

A) The linear function is: f(x) = -400x + 47,900.

B) The prediction for the population in 2018 is of 42,700.

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.

For this problem, we have that:

  • The initial population is of 47,900.
  • In 11 years, the population decayed to 43,500 from 47,900, hence the slope is given by: (43500 - 47900)/11 = -400.

Hence the function for the population in x years after 2005 is:

f(x) = -400x + 47,900.

2018 is 13 years after 2005, hence the prediction is:

f(13) = -400(13) + 47,900 = 42,700.

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

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