The rate of bacteria growth in a laboratory experiment was measured at 11% per hour. If this experiment is repeated and begins with 6 grams of bacteria, how much bacteria should be expected after 15 hours? Round to the nearest tenth of a gram.
Each hour the population rises by a factor of 1.11. So, after 15 hours, you have
6*1.11^15 = ?
To find the amount of bacteria after 15 hours, we can use the formula for exponential growth:
A = P(1 + r)^t
Where:
A = final amount of bacteria
P = initial amount of bacteria
r = rate of growth (in decimal form)
t = time (in hours)
In this case:
P = 6 grams (initial amount of bacteria)
r = 11% per hour = 0.11 (rate of growth in decimal form)
t = 15 hours
Substituting the values into the formula:
A = 6(1 + 0.11)^15
Now, let's calculate it step by step:
1 + 0.11 = 1.11
1.11^15 ≈ 4.06618
A ≈ 6 * 4.06618 ≈ 24.3971
Therefore, after 15 hours, we can expect approximately 24.4 grams of bacteria.
Remember, it's important to round to the nearest tenth of a gram, so the final answer is 24.4 grams.