*Use the following information to answer the next ques Consider the following functions y = x'+ • y = 2(3)* 1 7. y= 2* %3D y=-2 v = 4(-2)* * 1. How many of the above functions meet the conditions for the definition of an expone D. 5 В. З С. 4
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- If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2 where x, y,and z are measured in meters, and you are standing at a point with coordinates (60, 40, 966). The positivex−axis points east and the positive y−axis points north.If you walk northwest from point P, will you start to ascend or descend? At what rate? To answer this, do I need to make my function f(x,y) and then take the gradient, or do I need it to be f(x,y,z) and then take the gradient?Suppose that the demand for a product is given by q2p=6,000, where q represents the number of units of the product demanded and p represents the price per unit in dollars. a. Compute the elasticity of demand when the number of units demanded is 50 and the price per unit is $16. b. Is the demand elastic, inelastic, or unitary elastic? Could you look over my work? This should be solved using implicit differentiation. You solve for dq/dp and plug it into the function n=(-p/q)(dq/dp)
- If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f (x) = 1 / y (x), what is the average rate of change of the function f ( x) In the same period ?!3 7 - use logarithm differentiation to differentiate to find y prime (dy). y = xA) Differentiate y = 4√x + 8 / x - 6 / 3√x +10 B) Find the second derivative of y = 4 √x + 8/x - 6 / 3√x +10 C) Find the derivative of y = ( 1+x2 )x D) Find the derivative of f(x) = log3 5x2 + 1
- For number one, you need to find A. For extended delay type, input t as 24 then equal it to 0 (in this case, 10 is the limit for the extended type. Look at the graph) Then isolate A by dividing the function, so it should be 10/ (surge function). You can't do the same with medium and rapid since their limits are 100 and requires different time t value You need to take derivative to get t and then like before input the t value to the specific function and equal it to 100 to get A Number 2, I'm not too sure, but you need to compute integrals to get the area under the curve. The area is the maximum treatment effect. For Number 3a do another integral from O to 24 for the chosen delay type. For 3b compute an integral from. 24 to infinity. You're allowed to use a calculator for number 1 and 2 only via instructions provided I believe you must show your work for number 3 so I hope you are good doing improper integrals and integration by parts.Q 2: Use central difference method to estimate the 1and 2nd derivatives of the following function at x=3 and step size h=0.1. Compare your result with the true value (calculate the true error): f(x) = 25 x^3 – 6x^2 + 7x – 885th derivative of y = log x^5 to the base 2
- 1. Find the derivative of y = log7 (2 -3x) .Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. C(t) = (e−αt − e −βt )/(β − α) , where α and β are constants with β > α > 0. (a) Using the first derivative test, find when the maximum concentration occurs. (Your argument must use the first derivative test.) (b) When does the rate of change of concentration begin to increase? (Your answer should be supported by a rigorous argument.)Suppose that your friend, who is concerned that you are 100 pounds overweight, has studiedthe diet plan you started two months ago and is trying to get you to continue with the diet.He shows you the following function, which represents your weight w1t2 (in pounds):w1t2 = 300 - 15 ln1t + 12,where t is the number of months since starting the diet. He points out that the derivative of thefunction is always negative, so your weight is always decreasing. He claims that you cannothelp but lose all the weight you desire. Should you take his advice and use this diet plan?