The rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(t) = −0.18t2 + 3t + 15 gallons per year    (0 ≤ t ≤ 10), where t is the time in years since the start of 2000.† After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction f(t) =√0.2 + 0.04t  of all bottled water consumed in year t. Assuming that your model is correct, estimate,

Q: of tax returns that will be electronically filed for 2010 using exponential smoothing with α=0.1

A: Solution

Q: 1 In x dx =

A:

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A: Here we have to find the no of bacteria expected after two weeks.

Q: Suppose the income from an Internet access business is a continuous income stream with annual rate…

A: We have given the rate of annual flow,f(t)=900 t e-0.1t

Q: The half-life of Carbon-13 is 5750 years. Samples taken at an excavation site show that a one…

A:

Q: 6. Determine the equation for the following exponential function in the form of f(x)=ab* + c. Show…

A: Given problem:-

Q: Approximate to four decimal places f(x)=ex when x=-2.7183

A: Given function is f(x) = ex  Given that x = -2.7183

Q: 5. Complete the following table. FUNCTION f(x)=315(0.87)* f(x)=17(3)* Does the function. represent…

A: exponential decay function: y=a(1-b)x where y is the final amount, a is the original amount, b is…

Q: A culture of bacteria is growing at a rate of 5e0.bt per hour, with t in hours anc 0sts 20. How many…

A: The growth rate of culture is given as, dNdt=5e0.6t We need to find the new bacteria developed in…

Q: In mid to late March a COVID analyst predict the number of US cases could be modeled by the function…

A: Given: In mid late March a COVID analyst predict the number of US cases could be modeled by the…

Q: explain this.    the given height of a spaceship at time x is defined by h(x)=…

A:

Q: Solve for "X" 10000* = 1/100000

A: 10000x=1100000104x=10-5

Q: If the population of a country doubles in 90 years, in how many years will it treble under the…

A:

Q: suppose that the population (in millions of people) of a country is described by P(t)= 8.2(1.019)^t,…

A:

Q: A towns population, each year, can be modeled by the function P=12000(1.025)^t how fast, as a…

A:

Q: Consider the function f (x) = -x² + 10. Find the average rate of change in the interval -5 <x < -1.

A:

Q: A deposit earns interest at a rate of r percent compounded continuously and doubles in value in 10…

A: Given that, after 10 years, the initial amount is doubles, when the rate of interest r is compounded…

Q: Your cardiac index is your heart's output, in liters of blood per minute, divided by your body's…

A: a) Find the cardiac index of a 32-year old. Express the denominator in simplified radical form and…

Q: Suppose that E(X)=3 and E(X")=11. Then Var(3X+1)=

A: From the provided information, E (X) = 3 and E (X2) = 11

Q: 12. Which function describes exponential decay? c. Ax) = 25(0.8)* а. Ах) - 6(1.01)* b. Ax) =…

A: The solution is :

Q: A 50 000L tank can be drained in 30 minutes. The volume of water remaining in the tank after t…

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Q: 2. Determine the value of a so that the average rate of change of the function h(x) = 3x² + ax - 4…

A:

Q: he number of cases within 3 days due to coronavirus is as follows: 21 May 2020: 961 New Case 22…

A: (1a)   Let us consider the time values t as 1, 2, and so on. X: as the number of new cases.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.