Answer:
it takes 46 days to full the pond
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
[tex]y = 3.915(1.106)^x[/tex] is the regression equation where x is the number of days, y the the amount of water.
My answer:
As we can see in the equation:
- 3.915 is the initial value
- 1.106 = represents the increase in population at time x
this pond can hold up to 400 water lilies, it means that:
[tex]y = 3.915(1.106)^x = 400[/tex]
<=> [tex]\frac{400}{3.915}=(1.106)^x[/tex]
<=> [tex]102.17=(1.106)^x[/tex]
We convert to sides to log
<=> [tex]log(102.17)=log(1.106)^x[/tex]
<=> [tex]x=\frac{log(102.17)}{log(1.106)}[/tex]
<=> [tex]x=\frac{2.009}{0.0437}[/tex]
<=> x = 45.79
So it takes 46 days to full the pond
