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 1992.
A) 3.61 tons per hectare
B) 3.66 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 1992.
A) 3.61 tons per hectare 
B) 3.66 tons per hectare 
C) 3.75 tons per hectare 
D) None of the above

Quizplus · Accepted Answer

To estimate the yield in 1992, we need to find the average rate of change of yield between 1980 and 1992.

Average rate of change = (change in Y / change in t)

Change in Y = (4.11 - 3.32) = 0.79

Change in t = (25 - 0) = 25

Average rate of change = (0.79 / 25) = 0.0316

Now, we need to add this average rate of change to the yield in 1980 to estimate the yield in 1992.

Estimated yield in 1992 = (3.32 + 0.0316 * 12) = 3.66

Therefore, the best choice is B, which is 3.66 tons per hectare.

The Following Table Shows Average Rice Yield, in Tons Per