Population of Texas Texas was the third fastest growing state in the United States in 2016. Texas grew from 25.1 million in 2010 to 26.47 million in 2016. Use an exponential growth model to predict the population of Texas in 2025.

preprekomW 2021-02-12 Answered
Population of Texas Texas was the third fastest growing state in the United States in 2016. Texas grew from 25.1 million in 2010 to 26.47 million in 2016. Use an exponential growth model to predict the population of Texas in 2025.
You can still ask an expert for help

Want to know more about Exponential growth and decay?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Macsen Nixon
Answered 2021-02-13 Author has 117 answers

Given:
Texas grew from 25.1 million in 2010 to 26.47 million in 2016.
To predict the population of Texas in 2025 using an exponential growth model.
An exponential growth formula is given by,
P=P0ert −−−−(1)
where P is the total population after time t,
P0 is the starting population,
r is the rate of growth,
t is the time, and
e is the Euler's number.
Here,
P=26.47 million is the total population after time t=2016−2010=6 years,
P_0=25.1 million is the starting population, and t=6 years is the time.
Therefore,
26.47=(25.1)er(6)
e6r=(26.47)/(25.1)
ln(e6r)=ln(26.47)/(25.1)
by applying natural log on both sides
6rln(e)=ln(1.0546)
6r=0.0532
ln(e)=1
r=(0.0532)/(6)
0.0088
So to predict the population of Texas in 2025 using an exponential growth model, t=2025−2010=15 years.
Thus, equation (1) becomes,
P(15)=(25.1)e0.0088(15)
=(25.1)e0.132
(25.1)(1.1411)
28.6416 million
29 million

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions