Question

Wheat Production In Example 7 of Section 2.4, the U.S. corn production (in billions of bushels) was modeled by the function

p(t)=1.0757(1.0248)^t,
, where t was the time (in years) since 1930. Source: The New York Times Magazine.
(a) Find the average corn production from 1930 to 1950.
(b) Find the average corn production from 2000 to 2010.

Answer 1

Explanation:

Given that wheat Production In Example 7 of Section 2.4, the U.S. corn production (in billions of bushels) was modeled by the function

`p(t)=1.0757(1.0248)^t` where t was the time (in years) since 1930.

a) To find where t was the time (in years) since 1930.

The average value of any function f(x) in the interval (a,b) is given by

`(1)/(b-a) \int\limits^a_b {f(x)} \, dx`

We have1930 to 50 as t =0 to 20

`(1)/(20) \int\limits^20_0 {1.0757(1.0248)^t} \, dt`

=
`1.0757 (1.0248)^t)/ln (1.0248)\\= 43.911(1.63224-1)\\=27.762`

b) Here only limits change from 70 to 80

`1.0757 (1.0248)^t)/ln (1.0248)\\= 43.911(1.63224-1)\\=6.772`