Answer:
Around 27.2 years later
Step-by-step explanation:
This is compound decline problem. We use the formula:
[tex]F=P(1-r)^t[/tex]
Where
F is future amount (100)
P is present amount (229)
r is the rate of decrease (3% means 3/100 = 0.03)
t is the time in years (which we want to find)
So, lets substitute and solve:
[tex]F=P(1-r)^t\\100=229(1-0.03)^t\\100=229(0.97)^t\\0.4367=0.97^t\\ln(0.4367)=ln(0.97^t)\\ln(0.4367)=t*(ln0.97)\\t=\frac{ln(0.4367)}{(ln0.97)}\\t=27.2[/tex]
So, around 27.2 years later, the population would reach 100
