Question

The flowers in a basket become double after every minute. in one hour, the basket becomes full. after how many minutes, the basket would be half-filled

Answer 1

After 30 minutes the basket would be half - filled
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Answer 2

The time-taken for the basket to be half filled with flowers is 59 min.

Step-by-step explanation:

Given:

The number of flowers in the basket doubles every minute.

And time-taken to fill the basket completely = 60 min

To find = the time- taken for the basket to be half full

Solution:

We will take an exponential approach here.

Exponential growth is given by:

A= 1.$2^{m}$

Here, a= amount of flowers

M= Minutes

We have assumed that there is only one flower in the basket initially.

So, Flowers in the basket after 60 min:

A= 1.$2^{60}$

The time at which flowers will be half :

(1÷2)× $2^{60}$=  $2^{m}$

ln(1÷2)+ ln( $2^{60}$)= ln( $2^{m}$)

ln(1÷2)+ 60ln2= m.ln( 2)

-0.693+ 60×0.693 =m×0.693

On solving further,

m=59 min

Result:

Thus, the time-taken for the basket to be half filled with flowers is 59 min.

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