Answer:
46 days
Step-by-step explanation:
Given : Regression equation: [tex]y = 3.915(1.106)^x[/tex]
Where,
y = amount of water lilies the pond hold
3.915 = represents the initial population.
1.106 = represents the increase in population at time x.
x = is a variable of time.
The pond can hold 400 water lilies ⇒ y=400
Putting values in equation we get,
[tex]400 = 3.915(1.106)^x[/tex]
[tex]\frac{400}{3.915}=(1.106)^x[/tex]
[tex]102.17=(1.106)^x[/tex]
Taking log both side
[tex]log(102.17)=log(1.106)^x[/tex]
By logarithm property -[tex]loga^x=xloga[/tex]
[tex]log(102.17)=xlog(1.106)[/tex]
[tex]x=\frac{log(102.17)}{log(1.106)}[/tex]
[tex]x=\frac{2.009}{0.0437}[/tex]
[tex]x=45.97[/tex]
Approx. x=46
Therefore, 46th day the pond be full.
