To find the rate of change of Nathaniel's earnings, we can calculate his earnings per hour by dividing the total amount he earned by the total hours he worked.
The formula for the rate of change (in this case, the earnings per hour) is:
\[ \text{Rate of Change} = \frac{\text{Total Earnings}}{\text{Total Hours}} \]
Substituting the values:
\[ \text{Rate of Change} = \frac{847}{35} \]
Now, performing the division:
\[ \text{Rate of Change} = 24.2 \]
Thus, Nathaniel earned approximately $24.20 per hour.