The following table shows average rice yield, in tons per hectare, in Asia years since 1980. $$\begin{array} { | l | l | l | l | l | l | }
\hline \begin{array} { l }
\mathrm { t } = \text { years since } \
1980
\end{array} & 5 & 10 & 15 & 20 & 25 \
\hline Y = \text { yield } & 3.32 & 3.61 & 3.73 & 3.95 & 4.11 \
\hline
\end{array}$$ Use the average rate of change to estimate the yield in 1996.
A) 3.73 tons per hectare
B) 3.77 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. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \begin{array} { l } 
\mathrm { t } = \text { years since } \
1980
\end{array} & 5 & 10 & 15 & 20 & 25 \
\hline Y = \text { yield } & 3.32 & 3.61 & 3.73 & 3.95 & 4.11 \
\hline
\end{array}$$ Use the average rate of change to estimate the yield in 1996.
A) 3.73 tons per hectare 
B) 3.77 tons per hectare 
C) 3.87 tons per hectare 
D) None of the above

Quizplus · Accepted Answer

To estimate the yield in 1996, we need to find the average rate of change of yield over the period from 1980 to 1996, which is 16 years.

The average rate of change between t = 0 and t = 25 (i.e., the entire period from 1980 to 2005) is:

average rate of change = (final value - initial value) / (final time - initial time)
                        = (4.11 - 3.32) / (25 - 0)
                        = 0.03 tons per hectare per year
                        
Since the rate of change is constant over this period, we can use it to estimate the yield in 1996 as follows:

yield in 1996 = yield in 1980 + (16 years) x (average rate of change)
              = 3.32 + (16 x 0.03)
              = 3.80 tons per hectare
              
The closest choice is B) 3.77 tons per hectare.

The Following Table Shows Average Rice Yield, in Tons Per