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Read the scenario below.  What is the average rate of change from 20 to 30 hours and what does this mean?

In an experiment, a bacteria culture is monitored and its size in mg is recorded every 10 hours below:

To find the average rate of change of the bacteria culture's size between 20 and 30 hours, we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{\Delta \text{size}}{\Delta \text{time}} = \frac{\text{size at 30 hours} - \text{size at 20 hours}}{\text{30 - 20 hours}}
\]

From the table provided:
- The size at 20 hours is 44.6 mg.
- The size at 30 hours is 51.3 mg.

Now, we can calculate:

\[
\text{Average Rate of Change} = \frac{51.3 - 44.6}{30 - 20} = \frac{6.7}{10} = 0.67 \, \text{mg/hour}
\]

### Interpretation:
The average rate of change from 20 to 30 hours is **0.67 mg per hour**, which means that during this time period, the bacteria culture's size increased by an average of 0.67 mg every hour.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How do you calculate the average rate of change between different intervals of time?
2. What does the bacteria growth trend tell you about the conditions in the experiment?
3. How would the rate of change differ if you took data from other time intervals (e.g., from 0 to 10 hours)?
4. What could affect the bacteria's growth rate over time?
5. How can you model the bacteria's growth mathematically (e.g., with linear or exponential functions)?

**Tip:** Always check if the rate of change remains consistent across different intervals to determine if growth is linear or follows another pattern.

What is the average rate of change from 20 to 30 hours and what does this mean?

Learn how to calculate the average rate of change in bacteria culture size between 20 and 30 hours in this step-by-step example. Understand the implications of a 0.67 mg/hour increase, suitable for students in Grades 6-8.

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