Question

In Covina, California, the population is 47,000. The population increases 18% every year. Determine how long it will take to reach 192,000.

Answer 1

Answer: 8.5 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form)  =18/100 = 0.18

t= years

A = population after t years

Replacing with the values given:

192,000 = 47,000 (1+ 0.18)^t

Solving for t:

192,000/47,000 = 1.18^t

4.08 =1.18^t

ln 4.08 = ln 1.18^t

ln 4.08 =t (ln 1.18)

ln 4.08 / ln 1.18  =t

8.5 years = t

Feel free to ask for more if needed or if you did not understand something.