Hello, arturju!

A certain culture of bacteria intially contains 10,000 bacteria

and increases by 20% every hour.

Identify the explicit nth term of the sequence.

How many bacteria are in the culture at the end of 10 hours?

Let's baby-talk through this . . .

There areXbacteria.

At the end of an hour, there is 20% more bacteria, 0.20X more.

. . So there is: .X + 0.20X .= .1.2X bacteria

So the original amount in multiplied by 1.2 to give us the new amount.

Since this happensevery hour,

. . at the end of two hours, there are: .(1.2)²X bacteria

. . and at the end of three hours, there are: .(1.2)³X bacteria.

The problem says that: X = 10,000

Hence, at the end ofnhours, there are: .10,000·(1.2)^n bacteria

At the end of 10 hours: .10,000·(1.2)^10 .≈ .61,917 bacteria.