Denise places seven grams of yeast in a Petri dish and the d

Denise places seven grams of yeast in a Petri dish, and the dish, and the mass of yeast in the dish increase 3% per day for the next thirty days. Which of the following functions gives the mass M of the yeast as a function of the number d of days since Denise placed the yeast in the dish? (a) M(d) - 7 + .03d (b) M(d) = 7 + 1.03d (c) M(d) = 7 middot (0.03)^d (d) M(d) = 7.21^d (e) M(d) = 7 middot 1.03^d The Implied domain of the function y = f(x) = Squareroot 3x + 5/x - 1 is the set (a) [-5/3, + infinity] (b) All real numbers except x = 1 (c) All real numbers (d) (0, + infinity) (e) [-5/3, 1] U (1, +infinity) Based on the diagram below, which of the following statements is true? (a) theta -1 radian (b) theta 3.2 radians (c) theta 3 radians (d) theta -3 radians (e) theta 2.25 radians. If the point (3, 4) lies on the graph of an invertible function f, then which of the following points lies on the graph of its inverse function? (a) the point (4, 3) (b) the point (3, -4) (c) the point (3, 1/4) (d) the point (-3, -4) (e) the point (4, -3) What is the formula for the inverse of the function w = g(u) = 3Squareroot 3u - 1/5? (a) u = g^-1 (w) = (5w - 1/3)^3 (b) u = g^-1 (w) = 3w^3 - 1/5 (c) u = g^-1 (w) = 5w^3 + 1/3 (d) u = g^-1 (w) = 5 3 Squareroot w + 1/3 (e) u = g^-1 (w) = (3w - 1/5)^3

Solution

36) given growth rate r =3% =0.03

growth factor =1+0.03=1.03

initial mass =7 gms

mass after d days M =7(1.03^d)

mass after d days M =7*1.03^d

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37)f(x)= (3x+5)_/(x-1)

3x+5>=0 , x-10

x>= -5_/3, x1

domain is [-5_/3 ,1)U(1,+)

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38) -3 radians

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39)the point (4,3) lies on inverse function

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40)w =g(u)=³[(3u -1)_/5]

w =g(u)

=>g^-1(w) =u

³[(3u -1)_/5] =w

[(3u -1)_/5] =w³

(3u -1) =5w³

u=(5w³+1)_/3

u=g^-1(w) =(5w³+1)_/3