Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Find the derivative of each function. :r + 1 (a) me) = ln( ) _ 22(552 + l) (b) 903) _ m (0} M9?) = $32 The function M (t) = (a + (b a)ekmt)1/m is known as the von Bertalany function and was introduced in the 19305 by Austrian biologist Karl Ludwig von Bertalanffy. Calculate M '(0) in terms of the constants a, b, k and m. The energy (measured in ergs) associated with an earthquake of moment magnitude Mm are related by log10(E) = 16.1 + 1.5Mw. Calculate dE/de for M = 2, 5, 8. A particle moves counterclockwise around the ellipse with equation 9m2 + 16392 = 25. (a) In which of the four quadrants is rim/tit > 0? Explain. (b) Find a relation between rim/(it and dy/dt. (c) At what rate is the zit-coordinate changing when the particle passes the point {1,1} if its y- coordinate is increasing at a rate of 6 m/s'? Let L = h) be the amount of water (in liters) a species of tree needs per week when it is h centimeters tall. Some values are given in the table below. h 100 150 200 250 300 f(h) 2o 30 42 58 75 Let h = g(t) = 100 -+- D.1t2 be the height (in centimeters} of a particular tree of this species t months after January 1, 2020. (Assume this model is valid for the rst 6 years of the tree's life.) (a) Estimate f'(250). Give units. Explain the practical meaning in a sentence. (b) Calculate g'(39). Give units. Explain the practical meaning in a sentence. (c) Estimate (%f(g(t))) . Give units. Explain the practical meaning in a sentence. t=39 A parcel of air rising quickly in the atmosphere will decrease in temperature and increase in volume if it does not exchange heat with the surrounding air. For suiciently dry air, the relationship between temperature and volume is given by TV'U"1 = C' for a constant 0, temperature T in Kelvin, and volume V in cubic meters. Let time t be in hours. dT (a) Find and explain what it represents. Be sure to include units. dV dV (b) Find and explain what it represents. Be sure to include units. dT (c) Find % assuming that both T and V are functions of time, and explain what it represents. Be sure to include units