Question

The number of flowers in a tank doubles every day. It takes 30 days for the tank to swell. However, how long will it take to fill the tank half full?

Answer 1

Answer:

29th day

Step-by-step explanation:

The number of flowers in a tank doubles every day. It takes 30 days for the tank to swell.So,it will be half in 29tth day

Answer 2

ANSWER:-

I think that from a practical point of view, the answer in this particular case is: more or less, is 1 minute earlier.

For this answer, we could assume that the flow rate grows step by step, not continually.

In this case, we’re considering that the volume fills up in a sequence, in which each step represents 1 minute, and the flow rate is steady in that minute, but abruptly doubles at the start of the next minute:

$1 + 2 + 4 + 8 + 16 + 32 + 64 +...+ 2^{59}$

In this serie, if we compare the [math]n_{th}[/math] term, with the sum of the previous ones, we can see that the $n_{th}$ term is just one plus the sum of all the previous terms.

So, $2^{59} = (1 + 2 + 4 + 8 +...+ 2^{58}) + 1$

$as \: {2}^{59} \: is \: such \: a \: bigno.(5.8 \times {10}^{17})$

then the "+1" is really insignificant, so we can say that in the last minute, the volume doubles, and so, one minute before, the volume was half.

But, … oh, oh, mathematically speaking, that’s not exactly true!

Let’s say that the flow rate function is somethig like:

$fr = k \times {2}^{t}$

where t is expressed in minutes. You can see that the flow rate (FR) doubles every minute, and is a continuous function.

Then, the volume filled up after 60 minutes, if we begin with an empty tank, would be:

$v = k \times {f}^{60} _{0} \: {2}^{t} dt \: = k \times ( \frac{ {2}^{60} }{ln2} - \frac{1}{ln2)}$

For half the Volume, this yields to:

${2}^{x} = {2}^{59} + 0.5$

and x must be a little more than 59 minutes … nobody cares for such an small error if we say that is just 59 minutes!

But, for example, if instead of “the tank is full in 1 hour”, the question is “the tank is full in 5 minutes”, then the tank is half-full at 4 minutes and 2.7 seconds, which you can’t say it’s just 1 minute earlier at all!

By the way, if we consider that the initial flow rate is 1 drop of water ( 0.05 cc ) per minute, then 60mins later we have $5 \times {10}^{8} {m}^{3} /s.$

HOPE it's helps you ❤️

have a great day ❣️