Question

lets revisit the table from an earlier part of the lesson:
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

the average rate of change for the first 6 days is __________ square millimeters per day.
blank 1:

question 2 (1 point)
choose the statement that best describes how well the average rate of change decribes the situation.
a. the average rate of change accurately describes how the area changes each day.
b. the average rate of change is a better description for how the area changes each day than the data.
c. the average rate of change is not accurate because this is not a linear relationship.
d. i still dont know what the average rate of change means or how to find it.

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

For the first 6 days: $d_1=0$, $f(d_1)=1$; $d_2=6$, $f(d_2)=64$.

Step3: Calculate the average rate of change

$\frac{64 - 1}{6 - 0} = \frac{63}{6} = 10.5$

Step4: Analyze the relationship type

The function $f(d)=2^d$ is exponential, not linear. The average rate of change does not reflect the daily exponential growth.

Answer:

Blank 1: $10.5$
Question 2: c. The average rate of change is not accurate because this is not a linear relationship.