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 1997.
A) 3.73 tons per hectare
B) 3.82 tons per hectare
C) 3.87 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 1997.
A) 3.73 tons per hectare 
B) 3.82 tons per hectare 
C) 3.87 tons per hectare 
D) None of the above

Quizplus · Accepted Answer

The average rate of change for the yield from t=5 to t=10 is:
$$\frac{3.61-3.32}{10-5}=0.058$$
The estimated yield in 1990 (10 years since 1980) is:
$$3.32+0.058(10-5)=3.61$$
Similarly, the estimated yield in 1995 (15 years since 1980) is:
$$3.61+0.058(15-10)=3.90$$
Using the same average rate of change, the estimated yield in 1997 (17 years since 1980) is:
$$3.61+0.058(17-10)=3.82$$
Therefore, the answer is B, 3.82 tons per hectare.

The Following Table Shows Average Rice Yield, in Tons Per