At time t = 0, a seed is planted Aftert weeks, the height of the plant is given by f(t) = 0.3t² + 0.6t + 0.5 inches. At what rate is the plant growing after 8 weeks?

Q: leaks

A:

Q: A poplulation of 500 bacteria is introduced into a culture and grows in number according to the…

A: The growth of the population of 500 bacteria is given by the equation

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 s xs 60) where x is the…

A:

Q: Because of the absence of predators, the number of rabbits on a small island increases at a rate of…

A: Given that the growth function is: y(t) = y0ekt. At, t=0, y(0) = y0 [This is the initial…

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A:

Q: Q1 A balloon is rising vertically above a level, straight road at a constant rate of 2 ft sec. Just…

A: 1 Let the distance between bicycle and liftoff point be xt And distance between balloon and liftoff…

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

A: (b)

Q: The projected rate of increase in enrollment in a new college is estimated by dE/dt= ( at+1)^-1(…

A: Given the projected rate of increase in enrollment in a new college is dE/dt= ( at+1)^-1( a+1). We…

Q: It is estimated that a worker in a shop that makes picture frames can paint y frames t hours after…

A:

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: A 2,662-liter cistern is empty when water begins flowing into it (at t = 0) at a rate (in L/min)…

A: We have to find the function that gives amount of water in tank at time t.

Q: 4. The path of a baseball relative to the ground can be modelled by the function dlt) = – f² + 8t +…

A: derivative

Q: If a ball is thrown straight up with a velocity of 40 ft/s, its height (in ft) after t seconds is…

A: y=40t-16t2

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a…

A: use simple velocity,acceration,and distance formula.

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: Let's find.

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: Topic:- exponential growth function

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: the number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A: We use differentiation and integrations to solve this problem.

Q: Suppose that the amount (in gallons) of water in a tank is given by f(t) = 60e^−.1t, where t is in…

A:

Q: Suppose the quantity (in grams) of a radioactive substance present at time t is Q(t) = 2500 (5…

A:

Q: At time t ≥ 0, the velocity of a body movingalong the horizontal s-axis is v = t2 - 4t + 3. When is…

A: Given velocity of a body:

Q: A population of bacteria is growing according to the equation P(t) = 1950e" 10. Estimate when the…

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: 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in…

A: The growth rate of a colony of ants is given by 10t/(1+t2)2 Initially there are 100 ants ∴ Number of…

Q: If a rock is dropped from a 200 ft building, its posi- tion (in feet above the ground) is given by…

A: Given-  st=-16t2+200, where t is the time in seconds since it was dropped. To Find- (a) The velocity…

Q: The number of bacteria in culture is growing at a rate of r(t) = 3000e^0.6t. At t= 0, the number of…

A: Given rate at which no. of bacteria growing isr(t)=3000e0.6t

Q: The number of bacteria in a culture is given by the function n(t)=930e0.15tn(t)=930e0.15t where tt…

A: Comparing these two equations we get: P=930, r=0.15 So, continuous growth rate = 0.15= 15% And…

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 number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

A:

Q: Water is being pumped into a tank at the rate of r(t)= 30(1-e^(-0.16t)) gallons per minute, where t…

A: Water is being pumped into a tank at the rate of

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: 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: Suppose the depth of water in the lake at time t is given by h(t) = 5 -1/3t What is the average…

A:

Q: An oil storage tank ruptures at time t =0 and oil leaksfrom the tank at a rate of r(t)  = 100e-0.01t…

A: Given: Oil leaks from the tank at the rate r(t)= 100e-0.01t liters per minute. we have to find how…

Q: The position of a particle, with respect to an initial point, after t seconds is given by the…

A:

Q: It is estimated that a worker in a shop that makes picture frames can paint y frames t hours after…

A: The given function is: y=3t-8t2-t3, 0≤t≤4 where y is the number of frames painted in t hours. Here,…

Q: 4. The position of an object at time t is given by x = 34f - 8t + 2, where x is in feet and t is in…

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: A 12,000-liter cistern is empty when water begins flowing into it (at t = 0) at a rate (in L/min)…

A: Note: As per the guidelines we are supposed to answer only 3 sub parts, kindly repost the complete…

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 number of bacteria in a culture is given by the function n(t)=960e0.4tn(t)=960e0.4t where tt is…

A: Exponential Population model

Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

A:

Q: The number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

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: Find the derivative of the function. h(s) = −2√(5s2 + 3)

A: the given function is: hs=-25s2+3 we have to find the derivative of the given function.

Q: The population of a city (in millions) at time t (in years) is P(t)=2.8e0.008t, where t=0 is the…

A: Given data:   The expression for the given population at any time t is: P(t)=2.8e0.008t.     The…

Q: At time t=U years, a ranch has a population of 25 deer If the rate of growth of the population is…

A:

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

A: