Question

The total number of acres of genetically modified crops grown in developing countries from 2006 through 2012 was changing at the rate of $$R(t)=150 t+14.82 \quad(0 \leq t \leq 6)$$ million acres/year. The total number of acres of such crops grown in $2006(t=0)$ was 27.2 million acres. How many acres of genetically modified crops were grown in developing countries in $2012 ?$

Name: Problem 73, Chapter 6: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-07-31T23:57:57-08:00
Duration: 1 min 38 s
Channel: Lucas Finney
Description: The total number of acres of genetically modified crops grown in developing countries from 2006 through 2012 was changing at the rate of R(t)=150 t+14.82 (0 ≤t ≤6) million acres/year. The total number of acres of such crops grown in 2006(t=0) was 27.2 million acres. How many acres of genetically modified crops were grown in developing countries in 2012 ?

   The total number of acres of genetically modified crops grown in developing countries from 2006 through 2012 was changing at the rate of
$$R(t)=150 t+14.82 \quad(0 \leq t \leq 6)$$
million acres/year. The total number of acres of such crops grown in $2006(t=0)$ was 27.2 million acres. How many acres of genetically modified crops were grown in developing countries in $2012 ?$

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 6, Problem 73

Instant Answer

Solved by Expert Lucas Finney

07/31/2021

Step 1

82$ million acres/year. We are also given the initial condition that the total number of acres of such crops grown in 2006 (when $t=0$) was 27.2 million acres. Show more…

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The total number of acres of genetically modified crops grown in developing countries from 2006 through 2012 was changing at the rate of $$R(t)=150 t+14.82 \quad(0 \leq t \leq 6)$$ million acres/year. The total number of acres of such crops grown in $2006(t=0)$ was 27.2 million acres. How many acres of genetically modified crops were grown in developing countries in $2012 ?$

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Key Concepts

Rate of Change

This concept refers to the measure of how a quantity varies over time. In problems like this, a rate function (given in acres per year) quantifies the speed at which the number of acres changes, thereby setting up a relationship between time and the total quantity.

Definite Integration

Definite integration is a technique used to find the total accumulated change of a quantity over a finite interval. By integrating the given rate function over the specified time period, one can determine the total increase in acres.

Initial Conditions

Initial conditions provide the starting value of a function at a specific point in time. They are essential when solving an accumulation problem, as they allow the integration constant to be determined and ensure that the computed total change is added to the initial value to obtain the final result.

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