To determine

To find: the time ‘t’, when there are n bacteria

Answer

The inverse of this function is gn=3ln⁡2ln⁡n100.

Explanation

Calculation:

The number of bacteria after t hours is given as the function of t

n=ft=100.2t3

First, we write the function as

n=ft=100.2t3

Now, we solve this equation for t

n100=2t3

Applying the natural logarithmic on both sides, we have

ln⁡n100=ln⁡2t3

So,

ln⁡n100=t3ln⁡2

Then,

t=3ln⁡2ln⁡n100

gn=3ln⁡2ln⁡n100

This function shows the time ‘t’, when there are n bacteria.

Final staement:

The inverse of this function is gn=3ln⁡2ln⁡n100.

To determine

To find:

We have to find the time when population reaches 50,000.

Answer

The bacteria population reach 50,000 after 26.29 hours.

Explanation

Calculation:

Let the population reach 50,000 after t hours. So

t=3ln⁡2ln⁡50000100

Or t=3ln⁡2ln⁡500

So, t≈26.89

Thus, the population reach 50,00 after 26.89 hours.

Conclusion:

The bacteria population reach 50,000 after 26.29 hours.