Question

Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.

Answer 1

c: 0 < x < 60, -3.33

Explanation:

Answer 2

On average, the amount of bacteria decreases by 1 thousand every minute over the 100-minute period.

To estimate the domain of the function and solve for the average rate of change across the domain using the graph provided:

1. Estimate the Domain: The domain of a function represented by a graph is the set of all possible x-values, which corresponds to the "Amount of Time in minutes" axis in this graph. By looking at the graph, it appears that the domain starts at 0 minutes and extends to the rightmost point of the graph, which looks to be around 100 minutes. So we can estimate the domain as [0, 100].

2. Determine the Range: The range is the set of all possible y-values, corresponding to the "Amount of Bacteria in thousands" axis. From the graph, it seems that the range starts at just under 100 thousand (at time 0) and goes down to 0 thousand (close to time 100).

3. Calculate Average Rate of Change: The average rate of change is calculated using the formula
`\((\Delta y)/(\Delta x)\),` which is the change in the y-value divided by the change in the x-value over the interval.

4. Use the Endpoints for Calculation: To find the average rate of change, use the estimated values of bacteria count at the start and end of the time interval.

For example, if the bacteria count starts just below 100 thousand and goes down to 0 at the end of the domain, the change in y
`(\(\Delta y\))`is approximately -100 thousand (since the bacteria count is decreasing, this is a negative change). The change in x
`(\(\Delta x\))` is 100 minutes (from 0 to 100 minutes).

The average rate of change across the domain is then:

`\[\text{Average rate of change} = (\Delta y)/(\Delta x) = \frac{-100\text{ thousand}}{100\text{ minutes}} = -1\text{ thousand per minute}\]`