\begin{tabular}{l} Question 18 \ \hline You decide to save up for a vacation to Europe by throwing all of your loose change into a large coffee \ can. After a few months, you discover that the jar is 2 inches full and contains $$ \$ 202 $$. \ a) Determine the average rate of change in $$ \$ / $$ inch (Dollars per inch), for the coffee can from when it \ was empty ( 0 inches) to when it was 2 inches deep. \ The average rate of change from 0 to 2 inches is \ b) A month later, you check the can and find the change is now 3 inches deep arns adds up to $$ \$ 303 $$. Find \ the average rate of change, in $$ \$ / i n c h, ~ f o r ~ t h e ~ c o f f e e ~ c a n ~ f r o m ~ $$ \ 0 inches to 3 inches. \ The average rate of change from 0 to 3 inches is \ c) What is the meaning of the average rate of change in this situation? \ Select an answer \ Submit Question \end{tabular}

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**a)**  
The average rate of change is given by

$$
\text{Average rate of change} = \frac{\text{Change in dollars}}{\text{Change in depth in inches}}
$$

From 0 inches to 2 inches, the change in dollars is

$$
\$202 - \$0 = \$202,
$$

and the change in depth is

$$
2 - 0 = 2 \text{ inches}.
$$

Thus, the average rate of change is

$$
\frac{202}{2} = 101 \text{ dollars per inch}.
$$

**b)**  
From 0 inches to 3 inches, the change in dollars is

$$
\$303 - \$0 = \$303,
$$

and the change in depth is

$$
3 - 0 = 3 \text{ inches}.
$$

Therefore, the average rate of change is

$$
\frac{303}{3} = 101 \text{ dollars per inch}.
$$

**c)**  
In this context, the average rate of change represents the constant rate at which your savings are increasing as the jar fills. It means that, on average, every additional inch of coins in the coffee can corresponds to an increase of $$101$$ dollars in savings.
**a)** The average rate of change is $$101$$ dollars per inch. **b)** The average rate of change is $$101$$ dollars per inch. **c)** The average rate of change means that for every inch the jar fills, you save an average of $$101$$ dollars.

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