Question

here is the function f for clares moldy bread that you saw earlier.
d, time since mold spotting (days) | f(d), area covered by mold (square millimeters)
0 | 1
1 | 2
2 | 4
3 | 8
4 | 16
5 | 32
6 | 64
what is the average rate of change for the mold over the 6 days?
square millimeters per day
how well does the average rate of change describe how the mold changes for these 6 days?

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(d)$ over $[d_1,d_2]$ is $\frac{f(d_2)-f(d_1)}{d_2-d_1}$.

Step2: Identify values from the table

Here, $d_1=0$, $f(d_1)=1$, $d_2=6$, $f(d_2)=64$.

Step3: Substitute values into formula

$\frac{64 - 1}{6 - 0} = \frac{63}{6}$

Step4: Simplify the fraction

$\frac{63}{6} = 10.5$

The mold grows exponentially (doubling in area each day), so the average rate of change only gives an overall average of the growth over the 6 days. It does not reflect the actual daily growth pattern, which speeds up each day (the daily rate of change increases from 1 mm²/day on day 1 to 32 mm²/day on day 6).

Answer:

10.5 square millimeters per day

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