Bacteria are the most common example of exponential growth. The table below shows the number of E-Coli bacteria that would be present after each hour for the first six hours.

Hours Number of Bacteria
1 32
2 256
3 2048
4 16384
5 131072
6 1048567
When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time?

Could someone show me how to work this out please? Any help would be greatly appreciated! Thank you

256/32 = ?

2048/256 = ?

Answer: 8

Show your Work: 256/32=8
2048/256=8

the answer is 8

I really need help with this

What about the one asking us to find the number for 0?

For 0 is 4

The table shows the value y of a car after x years. Find the value after 12 years.

how what about slide number 5 i need help on that one

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To determine the number being multiplied each time, we can look for a pattern in the data. We can start by dividing the number of bacteria in each hour by the number in the previous hour. This will give us the same result for each interval if the growth rate is consistent.

Let's calculate the ratios for each interval:

Interval 1 (Hour 2 / Hour 1):
256 / 32 = 8

Interval 2 (Hour 3 / Hour 2):
2048 / 256 = 8

Interval 3 (Hour 4 / Hour 3):
16384 / 2048 = 8

Interval 4 (Hour 5 / Hour 4):
131072 / 16384 = 8

Interval 5 (Hour 6 / Hour 5):
1048567 / 131072 ≈ 8

As you can see, the ratio between the number of bacteria in each interval is approximately 8. Therefore, the number being multiplied each time is 8.

To verify this, let's check the calculation for the last interval:
131072 * 8 = 1048576

The result is very close to the actual number of bacteria in Hour 6 (1048567), confirming that the growth rate is indeed 8 for each interval.