Question

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.

Answer 1

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

Answer 2

• See below

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.