# is this the correct formula for me to solve this?

A bacteria culture has 2,000 bacteria. The number of bacteria increases by 5% each hour. How many bacteria are there after 12 hours?

2,000*0.05^(12-1)

## It is like compound interest (1+r)^n

2,000 * (1.05)^12

12 not 11 because it is at the END of the hour
at end of hour we have 1.05 times the initial amount the original + .05 * original = original (1 + .05)

## The formula you provided seems to be incorrect for calculating the number of bacteria after 12 hours. Let me correct and explain the correct formula for you.

To calculate the number of bacteria after a given period of time, you need to consider that the number of bacteria increases by 5% each hour. This means that each hour, the number of bacteria will be multiplied by 1.05 (100% + 5% = 105% = 1.05).

To solve this problem, you can use the following formula:

Final number of bacteria = Initial number of bacteria * (1 + growth rate)^number of hours

In this case, the initial number of bacteria is 2,000, the growth rate is 5% or 0.05, and the number of hours is 12. Substituting these values into the formula, we get:

Final number of bacteria = 2,000 * (1 + 0.05)^12

Now we can simplify and calculate the answer:

Final number of bacteria = 2,000 * 1.05^12

Let's calculate this using a calculator:

Final number of bacteria ≈ 2,000 * 1.795856542

Final number of bacteria ≈ 3,591.71

Therefore, after 12 hours, there will be approximately 3,591 bacteria in the culture.