Answer: 12 months
Step-by-step explanation:
Given : A tree double in weight in three months.
Since the weight is increasing by growth factor of 2 , therefore its is an exponential growth.
The exponential growth equation is given by :-
[tex]y=Ab^x[/tex] (1)
, where A is the initial values , b is the growth factor and x is the time period.
As per given , b= 2
Since the tree doubles in weight in three months, so time period x =[tex]\dfrac{t}{3}[/tex] , where t= number of months.
Substitute the value of b and x in (1) , we get
[tex]y=A(2)^{\dfrac{t}{3}}[/tex] , where y= weight of tree after t months and A is initial weight of tree.
When it will be 1600% of his initial weight , the weight of tree : y= 1600% of A =[tex]\dfrac{1600}{100}\times A=16A[/tex]
At y= 16 A , [tex]16A=A(2)^{\dfrac{t}{3}}[/tex]
[tex]\Rightarrow\ 16=2^{\dfrac{t}{3}}[/tex]
[tex]\Rightarrow\ 2^{4}=2^{\dfrac{t}{3}}[/tex]
[tex]\Rightarrow\ 4=\dfrac{t}{3}\Rightarrow\ t=3\times4=12[/tex]
Hence, it will take 12 months to be 1600% in weight.
