Chapter 3.4, Problem 24E

Remainder Round all answers to two decimal places unless otherwise indicated.

Rice production in Asia Improved agricultural practices, including better utilization of fertilizers and use of improved plant varieties, have resulted in increased rice yields in Asia. The accompanying table shows the average yield $Y$, in tons per hectare, as a function of the number of years $t$ since 1980.

$\mathit{t}=$ years since 1980	$\mathit{Y}=$ average yield
5	3.32
10	3.61
15	3.73
20	3.95
25	4.11

a. One study used a linear function to approximate yield as a function of time. Find an approximate linear model for $Y$ as a function of $t$.

b. Explain what the slope of the linear model tells you.

c. Use the model to calculate $Y\left(30\right)$, and explain in practical terms what your answer means.

d. What yield would the model estimate for 2025?

e. The 1993 report of the International Rice Research Institute predicted that rice requirements in Asis would grow exponentially. If the rice requirements in 2025 are 6.44 tons per hectare, will rice production in 2025 meet those requirements?