Science:Math Exam Resources/Courses/MATH102/December 2010/Question 01 (d)
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Question 01 (d) 

For this shortanswer question, only the answers (placed in the boxes) will be marked. A certain bacteria culture starts with 1000 bacteria, and the number of bacteria doubles every 10 minutes. If this continues indefinitely, how long (in hours) will it take for the population to reach 8 × 10^{15}? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The formula for continuous exponential growth is: where

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let denote the population size at time . The initial population size is 1000, and experiences exponential growth:
We know that the population doubles in 1/6 of an hour. We choose to measure in hours. Hence
Now knowing , we know the complete formula for the size of the bacteria culture at any time :
Finally, we solve for when the population reached to obtain
which is the time in hours (approximately 7.14 hours). 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. We can also calculate the answer using minutes instead of hours. The size of the bacteria culture at any time is calculated from the equation for exponential growth: . Using that the initial population size is initially 1000 and doubles in ten minutes we obtain:
Knowing we plug in the population size in question and solve for :
