Math 1425.P70 Examples for 3.5 & 3.6 Name 1)
Math 1425.P70 Examples for 3.5 & 3.6 Name _______________________________________________ Differentiate. 1) y = 6 x 2) f(x) = 210x 3) y = 1011x 4) y = 21-x 5) y = log5 x 6) f(x) = 2 log x 7) f(x) = log x 5 8) y = log(5x) 9) y = log5 (9x) Examples for 3.5 & 3.6 10) f(x) = x5 log7 x 11) f(x) = log7(x5 + 1) 12) f(x) = ex log4 x Solve the problem. 13) In one city, 29% of all aluminum cans distributed will be recycled each year. A juice company distributes 161,000 cans. The number still in use after time t, in years, is given by N(t) = 161,000(0.29)t. Find N'(t). 14) The magnitude R (measured on the Richter scale) of an earthquake of intensity I is defined as R = log I . I0 where I0 is a minimum intensity used for comparison. What is the magnitude on the Richter scale of an earthquake whose intensity, I, is 104 I0 ? 15) The intensity I of an earthquake is given by I = I0 10R, where R = the magnitude on the Richter scale, I0 is the minimum intensity, and R = 0 is used for comparison. Find I, in terms of I0 , for an earthquake of magnitude 4 on the Richter scale. Math 1425.P70 Examples for 3.5 & 3.6, page 2 16) The pH scale is used by chemists to measure the acidity of a solution. It is a base 10 logarithmic scale. The pH, P, of a solution is defined as P = - log10H, dP where H = [H3 O+ ] is the hydronium ion concentration in moles per liter. Find the rate of change . dH Differentiate. 17) f(x) = 4 5x 18) f(x) = 3 x7 19) y = 8xx2 20) y = (x + 1)x Math 1425.P70 Examples for 3.5 & 3.6, page 3 Find the elasticity. 21) q = D(x) = 500 - x 22) q = D(x) = 400 - 2x 23) q = D(x) = 1200 x 24) q = D(x) = 300 - x 25) q = D(x) = 700e-0.26x For the demand function given, find the elasticity at the given price and state whether the demand is elastic, inelastic, or whether it has unit elasticity. 26) q = D(x) = 600 - x; x = 91 27) q = D(x) = 300 - 4x; x = 65 28) q = D(x) = 1500 ; x = 49 x 29) q = D(x) = 600 - x; x = 560 Math 1425.P70 Examples for 3.5 & 3.6, page 4 Answer Key Testname: 1425_SECTION3_5__3_6 1) (ln 6)6 x 2) (ln 210)210x 3) 11 ∙ (ln 10) ∙ 1011x 4) (-ln 21)21-x 5) 1 x(ln 5) 6) 2 x(ln 10) 7) 1 x(ln 10) 8) 1 x(ln 10) 9) 1 x(ln 5) 10) x4 + 5x4 (log7 x) ln 7 11) 5x4 (ln 7)(x5 + 1) 12) ex 1 + log4 x x(ln 4) 13) N'(t) = 161,000(ln 0.29)(0.29)t 14) 4 15) 10,000 I0 16) dP 1 =dH Hln 10 17) (5ln 4 )4 5x 18) 7ln 3(x 6 ) 3 x7 19) 8xx 2 (2x ln 8x +x) 20) (x + 1)x ln(x + 1) + 21) E(x) = x 500 - x 22) E(x) = x 200 - x x x+1 23) E(x) = 1 24) E(x) = x 600 - 2x 25) E(x) = 0.26x 91 26) ; inelastic 509 27) 13 ; elastic 2 28) 1; unit elasticity 29) 7; elastic Math 1425.P70 Examples for 3.5 & 3.6, page 5
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