Question

A bacterium doubles every hour. There are 5 bacteria initially. How many will there be after 6 hours?

• A. 160 bacteria
• B. 320 bacteria
• C. 640 bacteria
• D. 460 bacteria

Hint:

In doubling problems, multiply initial quantity by $2^n$ where $n$ is the number of intervals.

Answer 1

The Correct Option is B

The problem involves an exponential growth process where the number of bacteria doubles every hour, starting with an initial count of 5 bacteria. We need to determine how many bacteria will be present after 6 hours.

To solve this, we use the formula for exponential growth:

\(N = N_0 \times 2^t\)

where:

• \(N\) is the final number of bacteria,
• \(N_0\) is the initial number of bacteria,
• \(t\) is the time in hours.

Given:

• \(N_0 = 5\) bacteria,
• \(t = 6\) hours.

Plug these values into the formula:

\(N = 5 \times 2^6\)

Calculate \(2^6\):

\(2^6 = 64\)

Thus,

\(N = 5 \times 64 = 320\)

Therefore, after 6 hours, there will be 320 bacteria.

The correct answer is: \(320\) bacteria.

This matches the provided answer option: 320 bacteria.