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?

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.