Julia S. answered • 07/20/21
Algebra I from a Long Term Sub
This problem will work using an exponential growth model. The general equation for exponential growth/decay is:
y=a(1+r)x
where y is the final number of bacteria, a is the initial amount of bacteria (what we're looking for in the first question), r is the rate of increase/decrease out of 1, and x is the number of time intervals.
Using this equation, we need to make sure we input the correct values. y will be the 70,000 final number of bacteria. A, our initial amount, is unknown, so we can leave it as such. r is the rate of increase as a percentage of 1, the whole. Since we're doubling, we're adding another whole, so r=1. X is our number of time intervals, and since it doubles every 10 minutes, after 110 minutes, we will have gone through 11 time intervals, so x is 11. Our equation should now look like this:
70,000 = a(1+1)11
Solving for a, we get an initial number of bacteria of 34.18.
We can use this initial value to determine the next question using the exact same equation. The only thing that's changing is our time interval. They now want to know y after 5 hours. Remember, our doubling time is in minutes. 5 hours is 300 minutes, which is 30 10 minute doubling intervals, so our X value will now be 30. Our equation should look like this:
y = 34.18(1+1)30
Plugging into our calcuator, we should get 3.67x1010 bacteria.
Julia S.
Unfortunately, 70,000 is not a perfect number to use 2^11 on. You start getting decimal bacteria’s around 2^6. The closest whole bacteria (34) would yield a similar doubling after 11 cycles of 69,632 bacteria, but this is not what they asked for. Rounding up to 35 gives 71,680. My guess is the question writer wanted to start with a nice whole number, regardless of how the math played out.07/20/21
Mark M.
How can you have 0.18 of a bacteria?07/20/21