Suppose it takes 6 hours for a certain strain of bacteria to reproduce by dividing in half. If 40 bacteria are present to begin with, the total number present after 𝑥 days is𝑓(𝑥)=40⋅16𝑥.Find the total number present after 1, 2, and 3 days.There will be bacteria present after 1 day, after 2 days and after 3 days.
Question
Suppose it takes 6 hours for a certain strain of bacteria to reproduce by dividing in half. If 40 bacteria are present to begin with, the total number present after 𝑥 days is𝑓(𝑥)=40⋅16𝑥.Find the total number present after 1, 2, and 3 days.There will be bacteria present after 1 day, after 2 days and after 3 days.
Solution
To find the total number of bacteria present after 1, 2, and 3 days, we need to substitute the values of x (which represents the number of days) into the function f(x) = 40 * 16^x.
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After 1 day: Substitute x = 1 into the function: f(1) = 40 * 16^1 = 40 * 16 = 640 So, there will be 640 bacteria present after 1 day.
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After 2 days: Substitute x = 2 into the function: f(2) = 40 * 16^2 = 40 * 256 = 10240 So, there will be 10,240 bacteria present after 2 days.
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After 3 days: Substitute x = 3 into the function: f(3) = 40 * 16^3 = 40 * 4096 = 163840 So, there will be 163,840 bacteria present after 3 days.
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