Calculus AB Assignment Practice with the Definite Integral as Accumulated Change 1. If r() is the rate of growth of a certain tree in feet per year where / is in years, what does the expression ] r(0)d represent? 2. A population of rabbits starts off at time / = 0 with 225 rabbits and increases at a rate of (() rabbits per month, where , is in months. A. What does the expression ($0 24 rod represent? B. What does the expression 225 + ," (par represent? C. Suppose you're told that ? for" roar = 4.25. How many rabbits are there in the population after 2 years?3. The marginal cost for producing & units of a certain product is given by the formula MIC = 0.001x4 - 0.5x + 66.5. A. What is the increase in the cost of the production if the production level is raised from 200 to 400 units? You may use your calculator here. Hint: Remember that marginal cost is the rate of change of the cost of production. B. What is the average cost per item of producing 330 items? You may use your calculator. 4. Below is a graph of the function ((x): 1234561 For what value of c > 0 is the average value of (x) on the interval [-5, ~] equal to 0? Explain your reasoning here, and don't use a calculator!Calculus AB Assignment Practice with the Definite Integral as Accumulated Change 5. Suppose a certain object moves in a straight line with the following velocity, where . is in meters per second and : is in seconds: v() = -2+ / + 3 sin(ni). Without using your calculator, but instead using properties of definite integrals and facts you know about area, determine the net change in distance of the object from time / = 0 to time "= 6 seconds and find the object's average velocity on this interval. 6. Below is the graph of y = (x) on the interval [0.#]: A. Based on the graph, put the following in order from least to greatest: B. Let / represent the average value of the function/(x) on the interval [0.6] Is there a value of c for which the average value of *x) on the interval [0. c] is greater than A? Explain why or why not