The deeper you are under water; the less sunlight reaches you. The percent of sunlight, P, that reaches a depth d, in metres, can be modelled by the function .

Q: The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is…

A: Given total cost ,                  (x)=-10x2+500x+110

Q: If the function y=e^-2x is vertically compressed by a factor of 3, reflected across the y-axis, and…

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Q: Graph the function f(x)=x after it has been vertically shifted 1 units.

A: Let y = x

Q: the number of bacteria in a culture was initially 8,000 and the number grew to 12,000 in 6 hours.…

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Q: Assume the annual rate of change in the national debt of a country (in billions of dollars per year)…

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Q: The percent P of surface light present under water is modelled by the function P = 100(0.975) where…

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Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=27x3            ⋯⋯1 In order to find the slope of the given…

Q: B(x) is the function that multiplied the input by 100 and subtracts by 5

A: This is normal question i thought you just want a function term

Q: Match the functions below with their graphs (A)-(F). (A) (B) (C) (D) (E) (F)

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Q: Use the graph of f(x) = e* below to complete part a and b below.

A: Given:- The function is, f(x)=ex and the graph is, To find: - The value of limx→-∞ex

Q: Find the slope of the graph of the function at the given point.

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Q: When given the equation for a function, how can you determinewhere it is increasing and where it is…

A: The derivative of a function may be used to determine whether the function is increasing or…

Q: Find the slope of the graph of the function at the given point.

A: Given function is  To find the slope of the above function at (1,4)

Q: If the function y = e4x is vertically compressed by a factor of 5, reflected across the x-axis, and…

A: Given function:

Q: On a recent scuba diving trip, Kate and Kara reached a depth of 130 feet. Six-and-a-half minutes…

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Q: The projected population of the United States for the years 2025 through 2055 can be modeled by  P…

A: States for the years 2025 through 2055 can be modeled by  P = 307.58e0.0052t,  where P is the…

Q: In the Andes Mountains in Peru, the number (N) of species of bats is the function of the elevation…

A: Given N=f(h) is the number of species of bats at an elevation h feet above the sea level

Q: Graph the function f(x)=x after it has been vertically shifted −4 units.

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Q: 2) f(x)= 2x x2+1

A: Sol:- Extreme Points of 2xx2+1First Derivative Test definitionSuppose that x=c is a critical point…

Q: 1. Determine, to the nearest tenth, the instantaneous rate of change of the function f (x) = 4x³ –…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Write the function defined by y=f(x),subject to the condition of the value of f(x) is 16 times the…

A: The function defined by y=fx , subject , to the condition of thevalue of fx is 16 times the value…

Q: The population of a pod of bottlenose dolphins is modeled by the function A ( t) 8(2)t , where t is…

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Q: Graph the accumulated empty seat miles from January 2002 to month t as a function of t, and use your…

A: From the data given by the Bureau of Transportation Statistics,  To find the accumulated empty…

Q: A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length…

A: We have to write the total cost C of construction as a function of h.

Q: The population of bacteria in one cubic centimeter of the blood of a sick person has been modeled by…

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Q: If the function y=e−2x is vertically compressed by a factor of 3, reflected across the y-axis, and…

A: given y=e-2x

Q: Find the point on the graph of the function f(x)= (x+1)? that is closest to the point (-5, 1) .…

A: Givenfx=x+12Closest to point −5,1

Q: If the function y=e−3x is vertically stretched by a factor of 4, reflected across the y-axis, and…

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Q: Find the point of the graph of the function that is closest to the given point: f(x) = 2x+9 ;…

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Q: The total cost of a ride, C, in British pounds (GBP), on BlackCabs can be modelled by the function C…

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Q: Find the slope of the graph of the function at the given input value. Round your answer to three…

A: Given that f(x)= 3x - 3x. And at x=6 find the slope of the graph of this function.     Here i…

Q: Suppose D defines the number of miligrams of drug concentration that is  present in the blood stream…

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Q: Write the equation of the parent function f(x) = x3 after it has been translated five units left,…

A: Given function We need to determine the function after f(x) has been translated 5 units left,…

Q: Evaluate the function at the indicated values.

A: Given ht=t+1t

Q: The triangular holes have a base of 3 inches and a height of h inches, and the other dimensions are…

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Q: In a biology experiment, there were 300,000 cells present initially and then the number started…

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Q: If the function y=e−x is vertically compressed by a factor of 2, reflected across the y-axis, and…

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Q: Use the graph to enter an equation for f(t).

A: In this problem, we have to find the path equation f(t) by using the given point and given equation…

Q: A 12-inch tall sunflower is planted in a garden and the height of the sunflower increases by 8% per…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks A 12-inch tall…

Q: t)=7(0.27)t, where the output f(t) measures the volume of liquid (in milliliters) in terms of is the…

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Q: The height of the corn stock in inches over the first eight weeks of growth could be roughly model…

A: The height of the corn stock in inches over the first eight weeks of growth could be roughly model…

Q: Suppose the number of bacteria in a culture is modeled by the function P(t) = 1750e0-1t, where t is…

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Q: Determine the rate of change for a function that has the solutions in the following K 3 0 2 -1 1 y…

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Q: Find the point on the graph of the function that is closest to the given point: f(x)= 2x+8; (0,18)

A: We have given f(x)= 2x+8; (0,18)

Q: Once to the top of El Capitan, 3,000ft hight, he used a rope to propel down. He descended at a rate…

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Q: Find the slope of the graph of the function at the given input value. Round your answer to three…

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Q: Consider the concentration, C, (in mg/liter) of a drug in the blood as a function of the amount of…

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Q: The total attendance at a contemporary art museum is modeled by the function f(x)=18,933(1.047)x. If…

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Q: Use the graph of the function below to answer the questions  a) is h(4) positive?  b) for which…

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Q: If the function y = e-2x is vertically compressed by a factor of 3, reflected across the y-axis, and…

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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.