Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door?

It would take 21 years for the population of Boomtown to reach 1 million people.

An exponential growth is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b is > 1

Let y represent the population of Boomtown after x years.

Given that initially there is a population of 475,000, hence a = 475000. Also, it is increasing at a rate of 3.75%, hence b = 100% + 3.75% = 1.0375

Hence:

y = 475000(1.0375)ˣ

For a population of 1000000:

1000000 =475000(1.0375)ˣ

2.1 = (1.0375)ˣ

xln(1.0375) = ln(2.1)

x = 21 years

Hence it would take 21 years for the population of Boomtown to reach 1 million people.

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After 20.22 years the population exceed 1 million people, if the population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.

Step-by-step explanation:

The given is,

           Population of Boomtown is 475,000

           Increasing at a rate of 3.75% each year    

           After few years population exceed 1 million people

Step:1

          Formula to calculate population with a given rate of increase,

                                       ..............................(1)

         Where,

                   F - Population after t years

                   P - Population at initial

                    r - Rate of increase

                    t - No.of years

        From the given values,

                      F = 1000000

                      P = 475,000

                       r = 3.75%

          Equation (1) becomes,

        Take log on both sides,

       Substitute log values,

                                      = 20.2216

                                   t ≅ 20.222 years

Result:

        After 20.22 years the population exceed 1 million people, if the population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.