Question

Regression equation: y = 3.915(1.106)x the pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day

Answer 1

46 Days

It said I have to have at least 20 characters to explain it well so here.
I hope you have a good day

Answer 2

46 days

Explanation:

Given : Regression equation:
`y = 3.915(1.106)^x`

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,

`400 = 3.915(1.106)^x`

`(400)/(3.915)=(1.106)^x`

`102.17=(1.106)^x`

Taking log both side

`log(102.17)=log(1.106)^x`

By logarithm property -
`loga^x=xloga`

`log(102.17)=xlog(1.106)`

`x=(log(102.17))/(log(1.106))`

`x=(2.009)/(0.0437)`

`x=45.97`

Approx. x=46

Therefore, 46th day the pond be full.