Assume that a store finds that its sales revenue changes at a rate given by S'(1) = -27t? +37t dollars per day, where t is the number of days after an advertising campaign ends and 0

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

A:

Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: Suppose that the profit (In dollars) from the sale of Kisses and Kreams is given by P(x, y) = 15x +…

A: Sale of Kisses Kreams is given by P(x, y)=15x+6.5y-0.004x2-0.015y2 where, x is the number of pounds…

Q: Suppose that t years from now, one investment plan will be generating profit at the rate of…

A:

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: As population is proportional to present population. So we need to form a differential equation. and…

Q: A population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day (t in days). Find…

A: Given that, The population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day. At…

Q: The yearly rate of consumption of natural gas (trillions of cubic feet) for a certain city is…

A:

Q: A factory can produce R rugs a month based on the function R(n) 4n2 – 7n +58, where n is the number…

A: Consider the given function of number of rugs: Rn=4n2-7n+58 Where, nx=15x+20x Rate change in rugs is…

Q: the number of U.S. Citizens aged 65 year and older from 1900 through 2050 is estimated to be growing…

A: Given: Rt=0.063t2-0.48t+3.87 As it is given that 0≥t≤15 Hence, t=0 for 1900 and t=10 for 2000 and…

Q: In a simple physical apparatus, the distance x cm and y cm are connected by the relation 1.1 1…

A: Distance x cm and y cm are connected by the relation 1x+1y=19 ....(1) x is increasing at the rate of…

Q: The number of bacteria growing in an incubation culture increases with time according to n(t) =…

A: The number of bacteria growing in an incubator culture increases with time according to the function…

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

Q: The rate of change of the volume V(t) of blood in the aorta at time t is given byV′(t) =…

A: Given data:The rate of change of the volume V(t) of blood in the aorta at time t is given by…

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: The revenue from a manufacturing process (in millions of dollars) is projected to follow the model R…

A:

Q: Water is pumped out of a holding tank at a rate of 7 – 7e-0.11t liters/minute, where t is in minutes…

A: NOTE: Refresh your page if you can't see any equations. . the water leaving the tank at a rate of…

Q: When a company produces and sells x thousand units per week, its total weekly profit is P thousand…

A: Given production level x=4+2t

Q: Suppose that a person learns y items in x hours, as given by y = 40/x, 0sxs 4. Find the rate of…

A: The given function is y=40x,   0≤x≤4. Obtain the derivative as follows.…

Q: Suppose a tank contains 8000 gallons of oil, and this is being pumped out at a rate of 600e ,-0.05t…

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Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1r dollars per…

A:

Q: As x increases uniformly at the rate of 0.002 feet per second, at what rate is the expression (1 +…

A:

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

A: a) Revenue per user at t = 0  = $ 350  Then it decreases by 10% every year, i.e. revenue per user at…

Q: Suppose that you have two resistors connected in parallel with resistances R1 and R2 so that the…

A: Rate of change can be found using Derivatives

Q: Supposed that the yearly rate of consumption of oil (in millions of barrels) is given by C'(t) =…

A:

Q: Suppose a model for the surface area of a human body is given by S = 0.1094w0.425,0.725, where w is…

A:

Q: Several years ago, ADTF Distributors purchased a brand new cargo plane to increase their coast to…

A:

Q: Suppose the rate at which consumers purchase peanut butter is increasing at a rate given by  f ′(t)…

A:

Q: The revenue (in millions of dollars) from a manufacturing process is projected to follow the model R…

A: Profit=Revenue-Cost

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: Answer is mentioned below

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: Based on the data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The weekly cost C, in dollars, for a manufacturer to produce q automobile tires is given by C = 2100…

A: Rate of change of cost function is the derivative of cost function with respect to time .

Q: 6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels…

A: Train E =120 miles per hour  Train N=90 miles per hour

Q: A cyclist riding at 5ms- 1 starts to accelerate, and 200 metres later she is riding at 7ms- 1. Find…

A: We know that the Third Equation of motion is    → v2 = u2 + 2as    ;     Where v = final velocity…

Q: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

A:

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

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

A:

Q: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

A: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

Q: The weekly cost C, in dollars, for a manufacturer to produce q automobile tires is given by C = 2300…

A: Answer: The solution is as given below:

Q: A pitcher of buttermilk initially at 27°C is to be cooled by settling in on a place where the…

A: At time t=0 minutes, temperature of buttermilk = 270C   At time t=20 minutes, temperature of…

Q: Find the PV of an income stream that pays out continuously at a rate R(t) = $5000e0.1t /year for 7…

A:

Q: Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to clear a road.…

A:

Q: A ball is thrown upward so that its height above the ground after time t is h(t) = 20t-5t, where h…

A: Given is : We have to find time when h(t) or height will be maximum And for height , function is :…

Q: 7. If f (t) = -t2 + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A:

Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula

Q: A factory produces bikes at a rate of 100 + 0.5t2 - 0.9t where t is in weeks, how many bikes were…

A: