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8. Given a circle's radius r = log5(t2+ t], time t a 1, determine the rate of Change at t = 10 for the following. [Hint: Area of a circle with radius R is nRZ] 8.1 The circle's radius relative to time t 8.2 The circle's area relative to time t 9. Given decay function A[t) = A[0] e'Kt, constant K > 0, A(0) > 0, and time t 2 0, and given that A'(10] = 4.55760 and A'(25] = -1.07052, evaluate the following. 9.1 MD) 9.2 A'(15.5] 9.3 Time t when A(t] and A'[t] = O 10. If revenue R(x] = -x2 + 10x + 20 and cost C(x) = 2x + 5, x > 0, production x in thousands of units, answer the following. [Hint: Prot = revenue cost and average profit = prot/x] 10.1 Production point that maximizes prot 10.2 Prot at the preceding point 10.3 Rate of change of prot at the preceding point 10.4 Average profit at the preceding point 10.5 Rate of change of average prot at the preceding point 10.6 Briey explain, in calculus terms, what conrms that the preceding point maximizes prot