Question

The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms. How long will it take for the population of the bacteria to reach 800?

Answer 1

The answer is to this problem would be 10.8.

Answer 2

16.34 hours

Explanation:

According to the given information we can see that the case is of exponential growth

Hence, we will use the formula

`A=P(2)^(t)/(24)`

Here A =800 is the amount that is needed to reach

P is the initial amount that is 500

We have to find the time it will take to reach 800 that is we need to find t

On substituting the values in the formula we get

`800=500(2)^(t)/(24)`

On simplification we get

`\Rightarrow(8)/(5)=(2)^(t)/(24)`

Taking log on both sides we get

`\Rightarrow\log(8)/(5)=\log(2)^(t)/(24)`

using
`\log(m)/(n)=\log m-\log n`

And
`\log a^m=m\log a`

`\Rightarrow\log{8}-\log{5}=(t)/(24)\log2`

Now substituting values of log 8=0.903, log 5=0.698 and log 2=0.301 we get

`\Rightarrow 0.903-0.698=(t)/(24)0.301`

`\Rightarrow 0.205=(t)/(24)0.301`

`\Rightarrow (0.205)/(0.301)\cdot 24=t`

`\Rightarrow t=16.34`