A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 7-hour 15 study session. The average rate of learning for the entire class was inversely proportional to the time spent studying, and was given approximately by V'(t) = - for 1Sts7. Find the area between the graph of V' and the t-axis over the interval [3,5], and interpret the results. (.. . The area between the graph of V' and the t-axis over the interval [3,5] is approximately. (Round to the nearest whole number as needed.) Interpret the results. Choose the correct answer below. O A. The area between the graph of V' and the t-axis over the interval [3,5] is the average number of words learned from t = 3 hr to t = 5 hr. O B. The area between the graph of V' and the t-axis over the interval [3,5] is the average difference between the rate of learning at t= 3 hr and the rate of learning at t = 5 hr. O C. The area between the graph of V' and the t-axis over the interval [3,5] is the average rate of learning for the entire class from t =3 hr to t = 5 hr.In order to study the effects of World War II on a certain country's economy, an economist used data from that country's census bureau to produce the following Lorenz curves for the distribution of income in 1935 and 1947. f(x) = xLorenz curve for 1935 g(x) = x Lorenz curve for 1947 Find the Gini index of income concentration for each Lorenz curve and interpret the results. What is the Gini index for 1935? (Round to three decimal places as needed.) What is the Gini index for 1947? (Round to three decimal places as needed.) Interpret your results. O A. Income was more equally distributed in 1947. O B. Income was more equally distributed in 1935. O C. Income was distributed the same in 1935 as in 1947.Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given by the following. 80 R(t) = t + 8 + 8; Osts 15 R(t) is the rate of production (in thousands of barrels per year) t years after pumping begins. Find the area between the graph of R and the t-axis over the interval [7, 12] and interpret the results. The area is approximately |square units. (Round to the nearest integer as needed.) Choose the correct interpretation of the results below. O A. Total production from the end of the first year to the end of the fifteenth year will be approximately 63 thousand barrels. O B. It will take approximately 64 years after pumping begins to reach a thousand barrels. O C. It will take approximately 63 years after pumping begins to reach a thousand barrels. O D. Total production from the end of the seventh year to the end of the twelfth year will be approximately 63 thousand barrels.Refer to the figure to the right. Set up a definite integral that represents the shaded area from a to b. . . . y=f (x)Find the area bounded by the graphs of the indicated equations over the given interval. y= - e"*; y=0; - 25xs2 . . . The area is square units. (Type an integer or decimal rounded to three decimal places as needed.)