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On the first day, there were 810 bacteria on a petri dish.
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Find, giving the answer to the nearest integer, the bacterial count after six days given the bacteria replicate daily.
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So in order to find a count, that means we’re finding the amount that’s there.
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So we’re adding everyday how much there actually is, and that’s called a summation.
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And this one is going to go on for six days.
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The formula for this summation will be: 𝑎 times one minus 𝑟 to the 𝑛 power divided by one minus 𝑟.
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So 𝑟 will represent our rate and it replicates daily.
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So it’s multiplying by two.
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So on the first day there might be one and on the next day there should be another one, so it’s twice as much.
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And then after that, the next day if it’s going to replicate what it already has, then you’re gonna add two.
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So now you have four.
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And then if you’re gonna replicate how much that is, you’re gonna add four again.
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So essentially, you’re just taking whatever number that it is and multiply it by two.
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𝑎 represents the initial amount that we have and that would be 810.
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And 𝑛 will represent the number of days how many times this is actually happening, and they’re six days; so 𝑛 is six.
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So we have 810 times one minus two the sixth power divided by one minus two.
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Two to the sixth power, 64 and one minus two is negative one.
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One minus 64 is negative 63.
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So now let’s take 810 times negative 63 and then divide by negative one, and we get 51030.
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Therefore, after six days, there will be 51030 bacteria in the petri dish.