Decide whether the following problem can be solved using precalculus or whether calculus is required. A bicyclist is riding on a path modeled by the function f(x) = 0.03(10x - x²), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 2. y 3 2 1 f(x) = 0.03 (10 x-x²) 1 2 3 4 5 6 7 8 X 9

Consider the function Y = (X*Z)0.5. At what point is the intersection of the line Z = - 1.4X + 30 with the contour line Y = 10? Graph the functions and their intersection

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)