At the beginning of an experiement, there are 100 bacteria in a certain culture. If the number of bacteria doubles every hour, how many bacteria will be in the culture at the end of 6 hours? A. 200 b. 600 c. 3200 d. 6400

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At the beginning of an experiement, there are 100 bacteria in a certain culture. If the number of bacteria doubles every hour, how many bacteria will be in the culture at the end of 6 hours? A. 200 b. 600 c. 3200 d. 6400

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Answer 1 · 2018-06-12T07:49:01

See explanation below

Explanation:

We have $100 = B_{0}$ $100=B_0$ bacteria at the begining in $t = 0$ $t=0$
In $t = 1$ $t=1$ , we will have $2 \cdot B_{0}$ $2·B_0$
In $t = 2$ $t=2$ we will have $2 \cdot 2 \cdot B_{0}$ $2·2·B_0$ and so on

In $t = n$ $t=n$ hours we will have $2^{n} B_{0}$ $2^nB_0$

We call $B_{n}$ $B_n$ to number of bacteria at n hours from begining. Then $B_{n} = 2^{n} B_{0}$ $B_n=2^nB_0$ is the general term

At 6 hours we will have $B_{6} = 2^{6} B_{0} = 64 \cdot 100 = 6400$ $B_6=2^6B_0=64·100=6400$

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At the beginning of an experiement, there are 100 bacteria in a certain culture. If the number of bacteria doubles every hour, how many bacteria will be in the culture at the end of 6 hours? A. 200 b. 600 c. 3200 d. 6400

1 Answer

Explanation:

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