Question

Select all the correct locations on the tables.

A zoo records the weight of a newborn elephant as 200 pounds. Each month, the elephant's current weight increases exponentially by half the
previous month's weight. Which equation can be solved to determine the number of months, it will take for the elephant to weigh 675 pounds?
How many months will it take?

Answer 1

`W_(n) =200[1+(50)/(100) ]^(n)`

3 months

Explanation:

The weight of the newborn elephant is 200 pounds.

Now, it's weight is increasing in each month by half the previous month's weight.

Hence, we can say that the weight of the elephant is increasing by 50% and it is compounded every month.

Therefore, the weight of the elephant after n successive months will be given by
`W_(n) =W_(0)[1+(50)/(100) ]^(n)`

⇒
`W_(n) =200[1+(50)/(100) ]^(n)` ... this is the required equation.

(Answer)

Now, if
`W_(n) =675`, then
`200[1+(50)/(100) ]^(n)=675`

⇒
`(1.5)^(n) =3.375`

Now, taking log on both the sides,

⇒ n log(1.5) =log(3.375)

⇒ n=
`(log(3.375))/(log(1.5))` = 3

Therefore, after 3 months the weight of the elephant will become 675 pounds. (Answer)