The following table shows average rice yield, in tons per hectare, in Asia years since 1980. $$\begin{array} { | l | l | l | l | l | l | }
\hline \begin{array} { l }
\text { t=years since } \
1980
\end{array} & 5 & 10 & 15 & 20 & 25 \
\hline Y = \text { yield } & 3.32 & 3.61 & 3.73 & 3.95 & 4.11 \
\hline
\end{array}$$ Use the average rate of change to estimate the yield in 1993.
A) 3.61 tons per hectare
B) 3.68 tons per hectare
C) 3.75 tons per hectare
D) None of the above

Question

The following table shows average rice yield, in tons per hectare, in Asia  years since 1980. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \begin{array} { l } 
\text { t=years since } \
1980
\end{array} & 5 & 10 & 15 & 20 & 25 \
\hline Y = \text { yield } & 3.32 & 3.61 & 3.73 & 3.95 & 4.11 \
\hline
\end{array}$$ Use the average rate of change to estimate the yield in 1993.
A) 3.61 tons per hectare 
B) 3.68 tons per hectare 
C) 3.75 tons per hectare 
D) None of the above

Quizplus · Accepted Answer

To estimate the yield in 1993, we need to find the average rate of change over the interval from 1980 to 1993 (which is 13 years). We can use the formula:

average rate of change = (final value - initial value) / (final time - initial time)

Plugging in the values from the table, we get:

average rate of change = (Y[25] - Y[5]) / (25 - 5) 
                       = (4.11 - 3.32) / 20 
                       = 0.0395

This means that on average, the yield increased by 0.0395 tons per hectare, per year, between 1980 and 1993. To estimate the yield in 1993, we can use the initial value of 3.32, and add the average rate of change for 13 years:

estimated yield in 1993 = 3.32 + 0.0395 * 13 
                       = 3.68

Therefore, the best choice is B, 3.68 tons per hectare.

The Following Table Shows Average Rice Yield, in Tons Per