. It is known from past experiments that the height in feet of a certain plant after t months is given approximately by H(t)=4 sqaure root t-2t; 0<t<2 How much time will it take for the plant to reach its maximum height? What is this maximum height?

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: At t= 1.824 hours , concentration will be maximum.....and its value = 0.47 microgram/ mL  For…

Q: For the function y = -2+5 sin (x-2), what is the maximum value?

A: Given,Function y =-2+5sinπ12(x-2)

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A: Suppose that copper is being projected to be extracted from a certain mine at a rate given by

Q: 2. A population of birds (in millions) t years from now is estimated by the following P (t) =…

A: Please see the answer below.

Q: The owner of a video store has determined that the profits P of the store are approximately given by…

A:

Q: Find the maximum sustainable harvest of the given function. f(S) = 24S025, where S is measured in…

A: Consider the given function fS=24S0.25 , where S is measured in thousands Suppose HS be the harvest…

Q: 4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle,…

A: We need to find rate of change.

Q: 2. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A:

Q: e a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a…

A: Given, saltwater with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water…

Q: Suppose a certain drug is administered to a patient, with the percent of a concentration of the drug…

A: Given that percent of a concentration of the drug is kt=5tt2+1 Differentiate kt=5tt2+1 with respect…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Given expression is PV1.4=C   ......1 Where P is pressure, V is volume and C is constant.  Pressure…

Q: A 2,916-liter cistern is empty when water begins flowing into it (at t=0) at a rate (in L/min) given…

A:

Q: It is known from past experiments that the height (in feet) of a given plant after t months is given…

A: Given that:                        Height of a given plant:          H(t)=4t12-2t…

Q: e) What are the domain and the range for this situation?

A:

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.1e0.007" , where t = 0 is…

A:

Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A:

Q: Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given…

A:

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.6e0.002t where t = 0 is the…

A:

Q: Consider the production function:           Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of…

A:

Q: For time t > 0, a particle moves along the x-axis, its position is given by the function s(t) = -t*…

A:

Q: The marginal cost function for the manufacture of wireless headphones is given by C'(x) = 34 −…

A: Given: Marginal cost function is given as:

Q: f(x)= Se-(at3)?-1

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given query is to find the maximum concentration of antibiotics in the blood during the first 12…

Q: a ball is thrown straight upwards from a tower ( 40 feet high) so thats its position, s in feet, t…

A: Given:A ball is thrown straight upwards from a tower ( 40 feet high) so that’s its position, s in…

Q: If a baseball is projected upward from ground level with an initial velocity of 160 feet per​…

A:

Q: Suppose that the concentration C of a medication in the bloodstream t hours after an injection is…

A: The concentration C of a medication in the bloodstream t hours after an injection is given by:…

Q: A 2000-liter cistern is empty when waterbegins flowing into it (at t = 0) at a rate (in L/min) given…

A: It is given that   . Suppose a quantity Q changes over time at a known rate Q'. Then the net change…

Q: The effectiveness of a medicine is given by E(t) = 2t In t³, where t is time in hours after…

A: Given,  The effectiveness of the medicine Et = 2t lnt3  Where t is time in hours   We have to find…

Q: If an object is projected upward from ground level with an initial velocity of 32 ft per​ sec, then…

A: A quadratic function is maximum or minimum at the vertex, which is x=-b/2a

Q: Solve parts a,b, and c.

A: Here we need to apply some basic concepts of derivatives to find the answers

Q: The rate of growth of a microbe population is given by m'(t) = 22t e ,2t where t is time in days.…

A: We will find the number of microbes in first two days.

Q: Y = 0.75X + 0.0042X2 – 0.00023x3 At what level of X, the output will be maximum?

A: Given: .

Q: o The population P(t) of a culture of bacteria is given by P(t) = -1,840 +81,000t + 10,000, where t…

A: The given function is, Pt=-1840t2+81000t+10000 For maximum population P'(t)=0. Then,…

Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7

Q: The equation y = log(x + 2) has a vertical asymptote at:

A: y=logx+2

Q: Suppose that the concentration C of a medication in the bloodstream t hours after an injection is…

A: To find the find the point of maxima find the critical points. critical points are the point where…

Q: 2. After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given query is to find the time at which concentration will be maximum.

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A:

Q: The volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t =…

A: Given that the volume of sphere is increasing at a rate proportional to the reciprocal of its…

Q: A 8,000-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A: Given the function for rate of water flowing is, Here t is measured in minutes. a. Given the time…

Q: (Q4) A small business has weekly profits of P(x) = x² + 4x – 2e", where x is the number of units…

A:

Q: Note: You may need to assume the fact that lim 1-0 for all n. MI The number of cell phone…

A: Given problem:- Note: You may need to assume the fact that limM→∞Mne-M=0 for all nThe number of cell…

Q: A 7,986-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A:

Q: The equation Y log(x – 1) has a vertical asymptote at:

A:

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A:

Q: The graph of the acceleration a(t) of a car measured in ft/s is shown. Use the Trapezoidal Rule with…

A:

Q: If an object is projected upward from ground level with an initial velocity of 160ft per​ sec, then…

A: given  s(t)=−16t^2+160t

Q: It is known from past experiments that the height (in feet) of a given plant after t months is given…

A: