Final answer:
The bacteria colony's growth rate, when calculated using the Rule of 70, is 14% over 5 days. To determine the daily growth rate, we calculate the equivalent daily rate to be approximately 13.3% when rounded to the nearest tenth.
Step-by-step explanation:
To determine the growth rate of a bacteria colony that doubles every 5 days, we can use the Rule of 70. The Rule of 70 states that to find the doubling time associated with a percentage growth rate, we divide 70 by the percentage growth rate. Therefore, if we know the doubling time, we can rearrange the formula to find the growth rate as a percentage.
Using the Rule of 70, we can set up the equation 70 = percentage growth rate × doubling time. Since we know the doubling time is 5 days, we can solve for the percentage growth rate as follows: percentage growth rate = 70 / 5. This gives us a growth rate of 14%.
However, we need to find the daily growth rate, not the overall rate for 5 days. To find the equivalent daily rate, we need to solve for a rate which, when applied for 5 consecutive days, results in the total 5-day growth of 14%. The equation is (1 + daily growth rate)5 = 1.14. Solving for the daily growth rate, we find it to be approximately 0.133 (or 13.3%). Rounded to the nearest tenth of a percent, the daily growth rate is 13.3%.
The bacteria colony's growth rate is 14% over 5 days. Calculating the daily equivalent, the growth rate is approximately 13.3% per day, rounded to the nearest tenth of a percent.