The shih-tzu population to reach 55,000 in 25.7 years.
For solving this question, you should apply the Population Growth Equation.
The formula for the Population Growth Equation is:
[tex]P_f=P_o\:\cdot \left(1\:+\:\frac{R}{100}\right)^t[/tex]
Pf= future population
Po=initial population
r=growth rate
t= time (years)
For this exercise, you have:
Pf= future population=55,000
Po=initial population =24,500 in 2016
r=growth rate= 3.2%
t= time (years)=?
Applying the Population Growth Equation.
[tex]P_f=P_o\:\cdot \left(1\:+\:\frac{R}{100}\right)^t\\ \\ 55000=24500\:\cdot \left(1\:+\:\frac{3.2}{100}\right)^t\\ \\ \frac{110}{49} =\left(1+\frac{3.2}{100}\right)^t\\ \\ t=\frac{\ln \left(\frac{110}{49}\right)}{\ln \left(\frac{103.2}{100}\right)}\\ \\ t=\frac{0.808}{0.0314} \\ \\ t=25.7[/tex]
Hence, t=25.7 years.
Read more about the population growth equation here:
https://brainly.com/question/25630111
