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Boston, Massachusetts had a population of 617,594 people during January 1 2010, and 675,647 people on January 1 2020.

Write an exponential function to represent the cities population, y, based on the number of years that pass, x after period of exponential growth. Describe The variables in numbers that you used in your equation.

Sagot :

Mhanifaidn

Answer:

  • See below

Step-by-step explanation:

Exponential function is:

  • y = abˣ

If we consider the time difference in years as x and the initial population as a, then we get:

  • 675647 = 617594*b¹⁰

Find the value of b:

  • b¹⁰ = 675647/617594
  • b¹⁰ = 1.09399864636
  • b = 1.09399864636^(1/10)
  • b = 1.009 (rounded)

The equation we got is:

  • y = 617594*1.009ˣ

Here we have y- population after x years since 2010, x - the number of years since 2010 and 1.009 is the population growth rate.

General equation

  • y=ab^x

Total years(x)=2020-2010=10

Now

  • 675647=617595b¹⁰
  • b¹⁰=675647/617595
  • b=1.009(Approx)

So.our equation

  • y=617595(1.009)^x
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