MATH HELP NEEDED (FINAL ANSWERS TYPED ASWELL) SO LOST

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The Monod growth function r(N) describes growth as a function of nutrient concentration N. Assume that r(N) = AN' N 2 0. Find the percentage increase when the nutrient concentration is doubles from N =0.1 to N=0.2. Compare this result with the findings when doubling the nutrient concentration from N =20 to N =40. This is an example of diminishing return. Cooo The percentage increase when the nutrient concentration is doubles from N=0.1to N=0.2 is |:|%. The percentage increase when the nutrient concentration is doubles from N=20to N=40is D%. The percentage increase from N=0.1toN=0.2is I:l the percentage increase from N =20 to N=40. (Round to two decimal places as needed.) X2 Let f(x) = > x 2 0. Complete parts (a) through (c) below. 16 +x () (a) Use a graphing calculator to graph f(x). Choose the correct graph below. All graphs have a window size of [0,10,1] by [0,10,1]. O A. /(I) /e o P O o P o o P The relationship between mammal body mass (M) measured in grams and resting heart rate (R) measured in beats per 1 minute is R(M) = 1180M 4 . This relationship is to be interpreted in a statistical sense; it does not exactly predict resting heart rate. Complete parts (a) through (c) below. 000, (a) Professor R.'s dog Molly weighs 20 kg. Predict Molly's heart rate from the formula for R(M). The heart rate is D beats per minute. (Round to the nearest whole number as needed.) A study found a power law relationship between land area and language diversity. Specifically, if A is the area of a region measured in km2 and D is the number of different languages spoken by the people occupying that region, then D=0.2A%% Use the given formula to complete parts (a) and (b) below. (@) (a) Estimate from this formula the number of languages spoken in the United States (area: 9.857 x 106 kmz). D languages (Type an integer or decimal rounded to three decimal places as needed.) The half-life of radium is 1690 years. If 70 grams are present now, how much will be present in 630 years? - - D grams (Do not round until the final answer. Then round to the nearest thousandth as needed.) Thulium 170 (Tm ) has a half-life of 129 days. Complete parts (a) through (c) below. . . . (a) If a sample of Tm10 has a mass of 400 micrograms, find a formula for the mass after t days. Choose the correct answer below. In 2 O A. W(t) = (400 p gr)e 129 days In 2 129 days O B. W(t) = 400 p gr 400 u gr O C. W(t) = In 2 129 days 129 days O D. W(t) = (400 p gr)e- In 2Which of the following functions is one to one (use the horizontal line test)? . . . Choose all that apply. A. f(x) = Inx, x > 0 B. f(x) =x , x20 c. f(x) = 21 X70 D. f( x) = 1x, x20 X E. f(x) = , X>0 F. f(X) = X, XER X(a) Show that f(x) = X2 + 7, x20, is one to one, and find its inverse together with its domain. (b) Graph f(x) and f 1 (x)in one coordinate system, together with the line y =x, and convince yourself that the graph of f 1 (x) can be obtained by reflecting the graph of f(x) about the line y =x. _ - (a) Which of the following graphs shows that f(x) = X2+ 7,x20is one to one? O B. O c. Fhl 1T 19 [TE]TP] 0 0 4 8 12 16 Find the inverse of the function together with its domain, and graph both functions in the same coordinate system. f(x)=2%, xER _ - The inverse function of 2% is f | (x)= |:| Simplify the following expressions. 3 log 6X (a) 6 (b) 2 3 log 2X 6 log 1/6X (c) 6 3 log 6X 3 log 1/6X log 1/6X (d) 36 (e) 6 (f) 36 . . . 3 log 6X (a) 6 =Simplify the following expressions. Write each expression as a single term using a single natural logarithm and without using any exponents. (a) Inx* + Inx-1 (b) Inx* - In x 2 5 1 (c) In (x2 - 16) - In (x+4) (d) - Inx 1 + Inx- . . . (a) In x* + Inx 1 = (Use integers or fractions for any numbers in the expression.)\fX Show that the function y = {E] can be written in the form y = ~ , where [ is a positive constant. Determine . (@) 1 X What is an appropriate formula, relationship, or property that can be used to transform the expression [E} into an expression of the form e~ M*? () A. The change of base formula, a* = X!"2 () B. The relationship between the exponential and logarithmic function, log aax =X () c. The property of logarithms, log asr =rlog ;s O D. The property of logarithms, log ,(st) = log ;s + log .t For the given pair of functions, use a graphing calculator to compare the functions. Describe what you see. y= sinx and y=3sinx Graph both functions in the same coordinate system. Choose the correct graph below. O A. O B. O C. ) D. ! Q ! Q ' Q ! Q 4 - - 4 4 \fGive a formula for N(t), t= 0, 1, 2, ..., on the basis of the information provided. No = 3; population doubles every 15 minutes; one unit of time is 15 minutes. . . . N(t) =