Question

Houston is the 4th largest city in the U.S. and the population within the metro area is continuing to grow.

In 2010 the population of the Houston metro area was 5.92 million. In 2017, the population was estimated at 6.89 million.
a. Find the population growth rate per year.
b. According to your estimated growth rate, in what year will the population of the Houston metro area double?

Answer 1

The population growth rate per year in the Houston metro area is 16.49%. According to the estimated growth rate, the population will double in 1 year.

Step-by-step explanation:

To find the population growth rate per year, we can use the formula:

Growth Rate = (New Population - Old Population) / Old Population

Using the given information:

Growth Rate = (6.89 million - 5.92 million) / 5.92 million = 0.1649 or 16.49%

Therefore, the population growth rate per year is 16.49%.

To determine in what year the population of the Houston metro area will double, we can use the formula:

Number of Years = log2(Double Population / Initial Population)

Using the given information:

Number of Years = log2(2 * 5.92 million / 5.92 million) = log2(2) = 1 year

Therefore, the population of the Houston metro area will double in 1 year.

Answer 2

a) 138,571.43 per year

b) 2067

Step-by-step explanation:

Population 2010 = 5.92 million

Population 2017 = 6.89 million

The time span is 7 years and the population grew by 6.89 - 5.92 = 0.97 million

1 million = 10⁶ = 1, 000, 000

0.97 million = 0.97 x 10⁶ = 0.97 x 1, 000, 000 = 970,000

a) population growth rate per year.

= 970000/7 = 138,571.43 per year

b) If this growth rate persists for the next years, and the population will double in n years , we get

Population in 2017 = 6.89 million

Double this value = 6.89 x 2 = 13.78 million

That means in n years the population should grow by 6.89 at the rate of 138,571.43 per year

Therefore
138,571.43 x n = 6.89 million

6.89 million = 6, 890, 000

So

138,571.43 x n = 6, 890, 000
n = 6890000/138571.43 = 49,72 years

Rounding this up we get the answer as approximately 50 years when the population will double to 13.78 million

That year would be 2017 + 50 = 2067