QUESTION 1

Suppose researchers have compared the following two models that are used to predict the weight of beef cattle of various ages, where W1 (t) and W2 (t) represent weight (in kilograms) of a tdayold beef cow. Answer parts (a) through (e) below. w1 (t) = 507.3 (1 0.944e' 00018") - 1.25 W2(t) = 497.1 (1 _ 05368 0.0mm) (a) What is the maximum weight predicted by each function? The maximum weight predicted by w1 (t) is 507.3' kg. (Type an integer or a decimal.) The maximum weight predicted by W2(t) is 497.1' kg. (Type an integer or a decimal.) (b) According to each function, nd the age that the average beef cow reaches 80% of its maximum weight. According to W1(t), the average beef cow reaches 80% of its maximum weight when it is about 825' days old. (Do not round until the final answer. Then round to the nearest integer as needed.) According to W2(t), the average beef cow reaches 80% of its maximum weight when it is about 797' days old. (Do not round until the final answer. Then round to the nearest integer as needed.) (c) Find W1 '(1100). Start by nding W1 '(t). Select the correct answer below and ll in any answer boxes to complete your choice. (Round to five decimal places as needed.) W1'(t)=e ("[11 to) " Wi'tt)=e "' * w1 '(t) = 0.90032 -e''0185"' W1'(t)= -e "'(1 -e l") Find w1'(1100). w1'(1100)= 011' (Round to two decimal places as needed.) Now, find W2'(1100). Start by finding W2 '(t). Select the correct answer below and fill in any answer boxes to complete your choice. (Round to five decimal places as needed.) XA. W2'(t)= e() O B. W2'(t) = . e (t) OC. W2'(t ) = e (1) ( 1 - e (1 ) ) * D. W2'(t) = 1.16714 - e - 0.00212 (1) (1 - 0.88600 . e - 0.00212 (1) ) 0.25000 Find W2'(1100). W2'(1100) = 0.11 (Round to two decimal places as needed.) Compare the results. The value of W,'(1100) is equal to the value of W2'(1100). (d) Graph the two functions, W, (t) and W2 (t), on [0,2500] by [0,700]. Choose the correct graph below. O A. O B. VC. O D.Comment on the differences in the growth patterns for each of these functions. Choose the correct answer below. The function W2(t) approaches its maximum and the function W1 (t) approaches its minimum. " There are no appreciable differences between the two graphs. Both approach their maximum asymptotically. The function W1 (t) approaches its maximum and the function Wz(t) approaches its minimum. There are no appreciable differences between the two graphs. Both approach their minimum asymptotically. (e) Graph the derivative ofthese two functions on [02500] by [0,1]. Choose the correct graph below. Q Q Q Q . ['1' ['7 ['7 1' pp Comment on any differences you notice between these functions. Choose the correct answer below. x There are no appreciable differences between the two graphs. Both approach their maximum asymptotically. There are no appreciable differences between the two graphs. Both approach their minimum asymptotically. The function W2'(t) starts out decreasing rapidly toward 0, while the function W1'(t) starts out increasing to a point before beginning to decrease toward 0 just as rapidly as W2'(t). * The function W1'(t) starts out decreasing rapidly toward a, while the function W2'(t) starts out increasing to a point before beginning to decrease toward 0 just as rapidly as W1 '(t). on The growth of the number of students taking at least one online course can be approximated by a logistic function with k = 0.0491 , where t is the number of years since 2002. In 2002 (when t = 0}, the number of students enrolled was 1.684 million. Assume that the number will level out at around 8.2 million students. (a) Find the growth function G(t) forthe number of students (in millions) enrolled in at least one online course. Find the number of students enrolled in at least one online course and the rate of growth in the number for the following years. (b) 2004 {c} 2011 (d) 2018 (e) What happens to the rate of growth over time? (a) Find (3(1). G(t) = (Type an exact answer in terms of e.) In a series resistance-capacitance DC circuit. the instantaneous charge 0 on the capacitor as a function of time (where t = 0 is the moment the circuit is energized by closing a switch) is given by the equation 0(t) = CV(1 ["0200 , where C, V, and R are constants. Further, the instantaneous charging current Ic is the rate of change of charge on the capacitor, or IC = dQldt. a. Find the expression for IC as a function of time. b. If C =10_ 5 farads, R =10? ohms, and V =10 volts, what is the charging current after 200 seconds? (Hint: When placed into the function in part a the units can be combined into amps.)