Question

Math To Do Ready

Properties of integer Exponents. Tutorial - Part 2. Level H

Follow the pattern. How many million bacteria were in the dish at

1 p.m. and 12 p.m.?

Hour Number of Bacteria (in millions)

12 p.m.

✓ DONE

1 p.m.

2 p.m.

3 p.m.

4 p.m.

32

6 p.m.

64

5 p.m.

Answer 1

• At 1pm, the number of bacteria in the dish is 1,000,000

• At 12pm, the number of bacteria in the dish is 500,000

Explanation:

Given the information on the table

`\left|\begin{array}c$Hour&$Number of Bacteria (in millions)\\---&--------------\\12 p.m.&\\1 p.m.&\\12 p.m.&\\2 p.m.&\\3 p.m.&\\4 p.m.&\\5 p.m.&32\\6 p.m.&64\end{array}\right|`

We are to follow the pattern to determine how many million bacteria were in the dish at 1 p.m. and 12 p.m.

Now:

`32=2^5\\64=2^6`

It therefore means that the bacteria population doubles every hour. Following this pattern and reducing the exponents by 1 backwards, we have:

`\left|\begin{array}c$Hour&$Number of Bacteria (in millions)\\---&--------------\\12 p.m.&2^(-1)=0.5\\1 p.m.&2^0=1\\12 p.m.&2^1=2\\2 p.m.&2^2=4\\3 p.m.&2^3=8\\4 p.m.&2^4=16\\5 p.m.&2^5=32\\6 p.m.&2^6=64\end{array}\right|`

Therefore:

• At 1pm, the number of bacteria in the dish is 1,000,000
• At 12pm, the number of bacteria is 0.5 million=0.5 X 1,000,000=500,000