Suppose 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)=2.613t2−17.7t+41.38 (0 ≤ t ≤ 6). The total number of acres of such crops grown in 1997 (t=0) was 18.1 million acres. How many acres of genetically modified crops were grown worldwide in 2012?

The number of acres of genetically modified crops were grown worldwide in 2012 is approximately 529.39 million.

Step-by-step explanation:

Note: There are mistakes in this question particularly in the years and the rate of change. The question is therefore correctly stated before answering the question as follows:

Suppose 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) = 2.613t^2 − 17.7t + 41.38 (0 ≤ t ≤ 6). The total number of acres of such crops grown in 2006 (t=0) was 18.1 million acres. How many acres of genetically modified crops were grown worldwide in 2012?

The explanation to the answer is now given as follows:

From the question, we are given:

R′(t) = 2.613t^2 - 17.7t + 41.38 (1)

Since t = 0 corresponds to 2006; by counting from 2006 to 2012, it implies that t = 6 corresponds to 2013.

Substituting t = 6 into equation to obtain the rate of change in 2012, we have:

R′(6) = (2.613* 6^2) - (17.7 * 6) + 41.38

R'(6) = 29.248

The number of acres of genetically modified crops were grown worldwide in 2012 can therefore be calculated as follows:

Number of acres grown worldwide in 2012 = Number of acres grown worldwide in 2006 * R'(6) (2)

Where;

Number of acres grown worldwide in 2006 = 18.1 million acres

R'(6) = 29.248

Substituting the values into equation (2), we have:

Number of acres grown worldwide in 2012 = 18.1 *  29.248 = 529.3888 million

Approximating to 2 decimal places, we have:

Number of acres grown worldwide in 2012 = 529.39 million

Therefore, the number of acres of genetically modified crops were grown worldwide in 2012 is approximately 529.39 million.