In t years, the population of a certain city grows from 300,000 to a size P given by P(t) = 300,000 + 6000t. dP a) Find the growth rate, dt b) Find the population after 10 yr. c) Find the growth rate at t= 10. d) Explain the meaning of the answer to part (c).

Q: The amount of trash G(t), in tons per year, produced by a town is projected to continue growing…

A: Here we do integration

Q: A car's distance in miles from its destination at time t is given by d = 360 - 55t How fast is the…

A: Rate of change of distance travelled from source with respect to time is known as velocity. So,…

Q: The position of a moving object is s(t)=t^3-2t^2-8t+5 feet away from 0 at t minutes. How long, in…

A:

Q: A body moves along a horizontal line in accordance to s t + 9t2 + 24t. Find the total distance…

A: Given query is to find the distance traveled by the body

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

A:

Q: The speed, s, of an accelerating object moving on a strait line is given by the formula: s = so +…

A: The initial speed is 10 m/s and the speed at time t is 16 m/s, so s0=10 m/s and s=16m/s. The time…

Q: In a railroad yard a 35,000 kg boxcar moving at 7.3 m/s is stopped by a spring-loaded bumper mounted…

A: We have to find how far does the spring compress (in cm) in stopping the boxcar.

Q: The height (in meters) of a projectile shit vertically upward from a point 4 m above ground level…

A: since you have posted multiple sub parts of a question in a single pic, As per our guidelines we…

Q: A 80-kg cyclist on a 19-kg bicycle starts coasting on level ground at 30 m/sec. Use v = vo e (-k/m)t…

A:

Q: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity of 125 ft/s.…

A: Given that: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity…

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Introductions :We have given an inverted pyramid.water rate = 55 cm3/secside length = 7 cm height =…

Q: A ball is thrown vertically upward with an initial velocity 15 m/s from an          initial height…

A: Use the kinematics equation to solve the problem and at the highest position the final velocity will…

Q: Consider an object in a surrounding with constant temperature of 25°C. If the emperature of the…

A:

Q: A Plane (Plane A) travels North at a speed of 800 kph. after 15 minutes, another plane (plane B)…

A: Planes are moving same direction :

Q: A surveyor is walking at the rate of 4 ft/sec along the diameter of a circular courtyard. A light at…

A: The radius Courtyard be a using in polar coordinates  r as a function of θ. Now, the equation of…

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 32 cm to a length…

A:

Q: a car move with an initial velocity of * 50 m/s to the right, determine its position when t=15 s, if…

A: This is a problem related to newton's law of motion. Based on the general formula and concept we…

Q: Assume the accleration of the object is a(t) = −32 feet per second per second. (Neglect air…

A:

Q: The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated…

A: Given: The volume V, in liters, of air in the lungs during a five-seconds respiratory cycle is…

Q: A bullet is fired perpendicularly upward from a gun and at an initial velocity of v0 = 300 m / s.…

A: Given that A bullet is fired perpendicularly upward from a gun and at an initial velocity of v0 =…

Q: ht h(t), in feet, of an airborne tee-shirt t seconds after being la ld a tee-shirt be airborne if it…

A: The height h(t) in feet, of an airborne tee-shirt t seconds after being launched is approximately…

Q: The forward motion of a SpaceX Dragon, t seconds after touchdown, is described by s(t) = 198t – ti,…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 3) If a spherical snowball melts so that its surface area decreases at a rate of 1 cm? he rate at…

A: It is given that a spherical ball melts so that its surface area decreases at a rate of 1 cm2 per…

Q: An object thrown downward from a 500-m cliff travels 57.2 m in 3 sec. What was the initial velocity…

A: We have to find the initial velocity of the object.

Q: In the given question as follows, assume the accleration of the object is a(t)= 32 feet per second…

A:

Q: The forward motion of a SpaceX Dragon, t seconds after touchdown, is described by s(t) = 198t – ti,…

A: Velocity and acceleration

Q: During a certain 12-hour period the temperature at time t (measured in hours from the start of the…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: On Earth, in the absence of air friction, a rock thrown vertically upward at a velocity of 64 feet…

A:

Q: Assume that the brakes of an automobile produce a constant deceleration of k ft/sec2. (a) Determine…

A: Given,          Assume that the brakes of an automobile produce a constant deceleration of k ft/sec2

Q: The equation for the amount Q of an antibiotic in the bloodstream at time t is Q = Ae-kt. %3D dQ 1.…

A: Q=Ae-kt Q is the amount of antibiotic in the bloodstream at time t Now we take derivative at time t…

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

A:

Q: An object is thrown straight up with a velocity, in ft/s, given by v(t)=−32t+47v(t)=−32t+47, where…

A:

Q: The edge length of a cube is 12 cm and increasing at a rate of 2 m. How fast is the Surface Area of…

A: Given dx/dt=2cm/hr X=12cm

Q: An object is thrown upward at a speed of 70 feet per second by a machine from a height of 13 feet…

A:

Q: A rocket rising from the ground has a velocity of v(t)=2,000 te-t/180 ft/s, after t seconds. How far…

A: Given thatThe velocity of the rocket rising from the ground is

Q: 31 An ice (ube is slowly melting, losing 3cm3 of water each hour. If it a lways remains a Perfect…

A: Volume of a cube=(side)^3

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: A car traveling at 60 mi/h (88 ft/s) skids 176 ft after its brakes are suddenly applied. Under the…

A:

Q: A cyclist rides down a long straight road with avelocity (in m/min) given by v(t) = 400 - 20t, for 0…

A: A cyclist rides down a long straight road with a velocity (in m/min) given by v(t)=400-20t, for…

Q: If a rock is thrown vertically upward from the surface of Mars with velocity 15 m/s, its height…

A: Given:         h=15t-1.86t2    Height of rock h(t)=25m        15t-1.86t2=25   rewrite in the form of…

Q: .A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 ft/sec. Use…

A:

Q: 4. The acceleration due to gravity is -9.8 meters per second squared. An object is thrown upward…

A:

Q: A chain lying on the ground is 10 m long and its mass is 60 kg. How much work (in J) is required to…

A:

Q: (a) Find a formula for the amount of yeast in the vat as a func- tion of t (measured in hours). (b)…

A: Formula for the ammount of yeast in tha vat as function of t:YF = Yi(2)t4 YF→Count of yeast after t…

Q: 2. Leanne is travelling at 13 km/hr. Fernando is moving at 3-5 m/s. Who is travelling faster?

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: Researchers in Alaska have developed models that can be used to estimate the mass of a polar bear.…

A: The equation relating mass and body dimensions is given as: M(x,y)=0.000199x1.2823y1.4874   Weight…

Q: 9. If a rock is thrown vertically upward from the surface of Mars with velocity 15 m/s, its height…

A: Height of the rock after t seconds which is thrown vertically upward from the surface of the Mars…

Q: A cyclist rides down a long straight road at a velocity (in m/min) given by v(t) = 400 – 20t, for…

A: Solve the following

Q: The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3…

A: the volume of the sphere is given by ..............(1)

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

A: Suppose that the length of rectangle is “l” and width is “w”   So according to the question, dwdt=2…