Question

World grain production was 1241 million tons in 1975 and 2048 million tons in 2005, and has been increasing at an approximately constant rate.

Answer 1

Answer:

The equation of line is $P(t)=26.9t+1241$

Step-by-step explanation:

Consider the provided information.

World grain production was 1241 million tons in 1975 and 2048 million tons in 2005,

We need to find the linear function.

The difference of the year is: 2005-1975=30

The function represents the world grain production at time t years after 1975, Thus, the first points is (0,1241) and the second points is (30,2048)

Find the slope of the line by using the formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute the respective values in the above formula.

$m=\dfrac{2048-1241}{30-0}\\\\m=\dfrac{807}{30}\\\\m=26.9$

The slope of the linear function is 26.9

The slope intercept form is: $y=mx+b$

Where b is the y intercept. y intercept is a point where the value of x is 0.

Therefore y intercept of the linear function is 1241 because the first points is (0,1241).

Hence, the equation of line is $P(t)=26.9t+1241$