Question

The number of bacteria in a dish grows by 10% each year. How many hours will it take for the number of bacteria to double?

Answer 1

To find out how long it will take for a population of bacteria to double when it grows at a rate of 10% per year, we can use the rule of 70 or the formula for exponential growth.

### Using the Rule of 70
The rule of 70 states that you can estimate the doubling time (in years) by dividing 70 by the annual growth rate (expressed as a percent).

Here, the growth rate is 10%, so we calculate:

\[
\text{Doubling Time (years)} \approx \frac{70}{10} = 7 \text{ years}
\]

### Converting Years to Hours
Now, we need to convert years into hours.

1 year = 365 days (not accounting for leap years)

1 day = 24 hours

Thus:

\[
\text{Doubling Time (hours)} = 7 \text{ years} \times 365 \text{ days/year} \times 24 \text{ hours/day}
\]

Calculating this gives:

\[
7 \times 365 \times 24 = 61,320 \text{ hours}
\]

### Conclusion
It will take approximately **61,320 hours** for the number of bacteria to double at an annual growth rate of 10%.