Question

Aimee is studying bacterial growth in the laboratory. She starts her experiment with 1 bacterium and then counts the bacteria at regular intervals and records them in the table below. If the pattern continues, how long will it take to have over 1000 bacteria?

$\center\begin{array}{|c|c|c|c|c|}\cline{1-5}\sf Time \ (hours) & \sf 0 & \sf 3 & \sf 6 & \sf 9\\\cline{1-5}\sf Number \ of \ Cells & \sf 1 & \sf 2 & \sf 4 & \sf 8\\\cline{1-5}\end{array}$

Answer 1

Given: Recordings of observations of bacteria.

To find: How long it would take to have 1000 bacteria.

Answer:

Let's consider the recordings of the number of cells.

1, 2, 4, 8, ... .

This can be written as 2⁰, 2¹, 2², 2³, ... .

Let's assume the powers to be 'n'. $\sf 2^n$ first crosses 1000 at 1024, where 'n' is 10.

Let's now observe the recording of the hours.

0, 3, 6, 9, ... .

Each time, the hour is increased by 3.

Through this, we understand that

At 0 hours, we have 1 (2⁰) bacteria.

At 3 hours, we have 2 (2¹) bacteria.

At 6 hours, we have 4 (2²) bacteria.

At 9 hours, we have 8 (2³) bacteria.

At 12 hours, we have 16 (2⁴) bacteria.

At 15 hours, we have 32 (2⁵) bacteria.

At 18 hours, we have 64 (2⁶) bacteria.

At 21 hours, we have 128 (2⁷) bacteria.

At 24 hours,we have 256 (2⁸) bacteria.

At 27 hours, we have 512 (2⁹) bacteria.



As mentioned earlier, $\sf 2^n$  first crosses 1000 at 1024 where 'n' is 10.

Therefore, after 30 hours, we'll have over 1000 (1024 ⇒ 2¹⁰) bacteria.