#### To determine

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

#### Answer

The inverse of this function is gn=3ln2lnn100.

#### 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

lnn100=ln2t3

So,

lnn100=t3ln2

Then,

t=3ln2lnn100

gn=3ln2lnn100

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

**Final staement:**

The inverse of this function is gn=3ln2lnn100.

#### 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=3ln2ln50000100

Or t=3ln2ln500

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.