Question

Write the rule for the table.

hours #of bacteria
1 32
2 256
3 2048
4 16384
5 131072
6 1048576

Answer 1

Did you notice that each number is a power of 2 ?

e.g.
32 = 2^5
..
16384 = 2^14
..
1048576 = 2^20

See what you can do with that hint

Answer 2

and look at the problem below this one :)

Answer 3

I'm still a little lost

Answer 4

I see that it is 2^x = the # of bacteria but i'm still stuck

Answer 5

let's look at the exponents of your given data

32 = 2^5
256 = 2^8
2048 = 2^11
16384 = 2^14
131072 = 2^17
1048576 = 2^20

so the exponents are 5, 8, 11, 14, 17, 20
they are an arithmetic sequence with a = 5 and d = 3
term(n) = a + (n-1)d
= 5 + (n-1)(3) = 3n +2 <==== general expression for your exponent

so number of bacteria = 2^(3x + 2)

Answer 6

Thank you so much for your help!!

Answer 7

[AI-generated answer — Explain Bot]

To determine the rule for the table, we need to analyze the relationship between the number of hours and the number of bacteria.

Looking at the given data, we can observe that the number of bacteria is increasing exponentially with each hour. In each step, the number of bacteria appears to be multiplying by 8.

Let's break it down step by step:

- In the first row, when there is one hour, there are 32 bacteria.
- In the second row, when there are two hours, the number of bacteria has multiplied by 8, resulting in 256 bacteria.
- In the third row, when there are three hours, the number of bacteria has again multiplied by 8, resulting in 2048 bacteria.
- This pattern continues for the remaining rows.

So, the rule for the table can be expressed as follows:

Number of bacteria = 32 * (8 ^ (hours - 1))

Here, '^' represents exponentiation, and '(hours - 1)' indicates that the exponent increases by 1 as the hours increase.

Using this rule, we can find the number of bacteria for any given number of hours.