# How many bacteria will be present after 5 hours if a culture of bacteria obeys the law of uninhibited growth where if 500 bacteria are present in the culture initially and there are 800 after 1 hour?

##### 3 Answers

THe number of bacteria is

#### Explanation:

The growth of bacteria is according to the differential equation

Integration of this equation yields

or

The initial conditions are

Also,

Therefore,

Therefore,

Therefore,

After

#### Explanation:

We need to find an equation of the form:

Where:

We have:

Using these values:

We now solve for

Divide by 500:

Taking natural logarithms of both sides:

Hence:

And:

This simplifies to:

Amount of bacteria after 5 hours:

If it obeys the law of uninhibited growth, growth occurs **exponentially** .

With

#B(t) = B_o a^t qquad {(a in RR), (a gt 1):}#

Use the given condition to find

Then after 5 years:

Then round that to a whole number of bacteria :)