The rate of bacteria growth in a laboratory experiment was measured at 14% per hour. If this experiment is repeated and begins with 7 grams of bacteria, how much bacteria should be expected after 15 hours? Round to the nearest tenth of a gram.
To find the amount of bacteria after a given number of hours, you can use the formula for exponential growth:
A = P(1 + r)^t
Where:
A is the final amount of bacteria
P is the initial amount of bacteria
r is the growth rate (expressed as a decimal)
t is the time in hours
In this case, the initial amount of bacteria is 7 grams, the growth rate is 14% per hour (or 0.14 as a decimal), and the time is 15 hours.
Substituting these values into the formula:
A = 7(1 + 0.14)^15
Let's calculate it step by step:
1. Add 1 to the growth rate:
1 + 0.14 = 1.14
2. Raise this value to the power of the number of hours:
1.14^15 ≈ 6.173
3. Multiply the result by the initial amount of bacteria:
7 * 6.173 ≈ 43.211
After 15 hours, approximately 43.2 grams of bacteria should be expected.
Please note that the answer is rounded to the nearest tenth of a gram, as specified in the question.