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\fStep 5 of 5 In order to solve the numerator equal to zero, set all factors equal to zero and solve for x. 2[In x331r1e In x} = n {lnx 31 = EEEEEI [1-52 I 18. [BB Points] DETAILS PREVIOUS ANSWERS OSEALC1 3.9.360. An isotope of an element has a halflife of approximately 18 hours. Initially there are 15 grams of the isotope present. (a) 1.\"Ifn'te the exponential function, QR), that relates the amount of substance remaining as a function of t, measured in hours. I (b) Use part {a} to determine the rate at which the substance is decaying in t hours. Q'UJ = 15300385: K (c) Use part {b} )to determine the rate of decay {in gfhr) at t = 6 hours. [Round your answer to four decimal places.) _x mm 19. [0/2 Points] DETAILS PREVIOUS ANSWERS OSCALC1 3.9.362. The relative rate of change of a differentiable function y = f(x) is given by 100 . f(X]%. f(x) One model for population growth is a Gompertz growth function, given by P(x) = ae-b . where a, b, and care constants. (a) Find the relative rate of change formula for the generic Gompertz function. bee -be - CX Xdy Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dx ( 7 + ye ) = (7x + e ) dx dx (vel + el)dy dx =7+e* ((1je(]) + e(1) dy = 7+ e(1) dx dy 2e =7+e dx O dx X What is the slope of the tangent line to the curve 7 + yel = 7x + e* at the point (1, 1) for the equation 7 + yel = 7x+ e*? dy = dx