Question

1. with the help of scientists, farmers in the philippines have been able to produce more and more grain per hectare each year. here are the crop yields for several years:

the crop yield can be described by the equation ( y = 46.7x - 9000 ) where ( x ) is the year and ( y ) is the grain yield in kilograms per hectare (kg/ha).
a) according to the model, what was the crop yield in 1969? round your answer to the nearest whole number.
b) assuming that this trend continues, what crop yield is predicted for the year 2029 by the model? round your answer to the nearest whole number.

Explanation:

Step1: Substitute \(x = 1969\) into the equation \(y = 46.7x-9000\)

Substitute \(x = 1969\) into \(y=46.7x - 9000\), we get \(y=46.7\times1969-9000\).
First, calculate \(46.7\times1969\):

$$
LATEXBLOCK0
$$

Then \(y = 91952.3-9000=82952.3\approx82952\)

Step2: Substitute \(x = 2029\) into the equation \(y = 46.7x-9000\)

Substitute \(x = 2029\) into \(y = 46.7x-9000\), we get \(y=46.7\times2029-9000\)
First, calculate \(46.7\times2029\):

$$
LATEXBLOCK1
$$

Then \(y=94754.3 - 9000=85754.3\approx85754\)

Answer:

a) \(82952\) kg/hectares
b) \(85754\) kg/hectares