# A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it take for the bacteria count to reach 100?

##### 2 Answers

**It will take** **hour to reach** **bacteria.**

#### Explanation:

Formula for exponential growth is

Where

sides we get

on both sides we get

It will take

Another method to find it will take an additional

#### Explanation:

Let's have a go at doing this without (explicitly) taking logarithms, etc.:

Note that:

#sqrt(10) = 3+1/(6+1/(6+1/(6+...))) ~~ 3+1/6 = 19/6#

Denote the time in hours by

Let

We are given:

#{ (p(0) = 50), (p(2) = 80) :}#

What is

If the rate of growth is constant then

#p(1) = sqrt(p(0) * p(2)) = sqrt(50*80) = sqrt(4000) = 20sqrt(10)#

So every hour, the population increases by the factor:

#(p(1))/(p(0)) = (20sqrt(10))/50 = (2sqrt(10))/5#

We find:

#p(3) = 80 * (2sqrt(10))/5 = 32sqrt(10) ~~ (32*19)/6 = 101 1/3#

So there will be

Let's linearly interpolate the last hour:

We want about