The constant rate of continuous growth, k, for this population is equal to 2.11935%. And the population will reach 250,000 people in 24.36 years.
For solving this question, you should apply the Population Growth Equation.
Population Growth Equation
The formula for the Population Growth Equation is:
[tex]P_f=P_o*(1+\frac{R}{100} )^t[/tex]
Pf= future population
Po=initial population
r=growth rate
t= time (years)
STEP 1 - Find the constant rate of continuous growth, k, for this population.
For this exercise, you have:
Pf= future population= 185,000 in 2020.
Po=initial population =150,000 in 2010.
r=growth rate= ?
t= time (years)=2020-2010=10
Then,
[tex]P_f=P_o*(1+\frac{R}{100} )^t\\ \\ 185000=150000\cdot \left(1+\frac{R}{100}\:\right)^{10}\\ \\ \left(1+\frac{R}{100}\right)^{10}=\frac{185000}{150000} \\ \\ \left(1+\frac{R}{100}\right)^{10}=\frac{37}{30}\\ \\ R=100\sqrt[10]{\frac{37}{30}}-100=2.11935\%[/tex]
STEP 2 - Find the t for population 250,000 people.
[tex]P_f=P_o*(1+\frac{R}{100} )^t\\ \\ 250000=150000\cdot \left(1+\frac{2.11935}{100}\:\right)^{10}\\ \\ \left(1+\frac{2.11935}{100}\right)^{10}=\frac{250000}{150000} \\ \\ \left(1+\frac{2.11935}{100}\right)^t=\frac{5}{3}\\ \\ t\ln \left(1+\frac{2.11935}{100}\right)=\ln \left(\frac{5}{3}\right)\\ \\ t=\frac{\ln \left(\frac{5}{3}\right)}{\ln \left(\frac{102.11935}{100}\right)}\\ \\ t=24.36[/tex]
Read more about the population growth equation here:
brainly.com/question/25630111
