Question

A tree double in weight in three months. How long will it take to be 1600% in weight? (Linear or exponential growth?)

Answer 1

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 :-

$y=Ab^x$   (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 =$\dfrac{t}{3}$ , where t= number of months.

Substitute the value of  b and x in (1) , we get

$y=A(2)^{\dfrac{t}{3}}$ , 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 =$\dfrac{1600}{100}\times A=16A$

At y= 16 A , $16A=A(2)^{\dfrac{t}{3}}$

$\Rightarrow\ 16=2^{\dfrac{t}{3}}$

$\Rightarrow\ 2^{4}=2^{\dfrac{t}{3}}$

$\Rightarrow\ 4=\dfrac{t}{3}\Rightarrow\ t=3\times4=12$

Hence,  it will take 12 months to be 1600% in weight.