The exponential function  N = 3.93 × 1.34d  gives the approximate U.S. population, in millions, d decades after 1790. (The formula is valid only up to 1860.) (a) What is the yearly growth factor?  Find a formula that gives the population y years after 1790. (b) What is the century growth factor? (Round your answer to two decimal places.) Find a formula that gives the U.S. population c centuries after 1790. (Assume that the original formula is valid over several centuries.)

Q: 6. Let f(a) %3D |x + 4), g(a) — а? — 4х, h(х) functions and their domains, or evaluate the expressio...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

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A: From x-y=-10 we get:  

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Q: A population, P(t) (in millions) in year t, increases exponentially. Suppose  P(9)=21 and P(17)=28. ...

A:

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A:

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A:

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A: To express 7 over 16 as decimal we divide 7 by 16

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A:

Q: Consider the following quadratic function. f(x) = −4x2 + 6x − 8 Find the vertex. (x, y)=

A: To determine the vertex of the equation.  

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A:

Q: 2log(base 2)(x-8)-log(base 2)x=2

A: Given,

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A: Number of subsets of a set with n elements is 2n Given that n=6 So, number of subsets= 26=64  

Q: Consider g(x)=-3(1/5)x + 2 of the function f(x)=(1/5)x. sketch the graph of g(x)

A:

Q: Question #3

A: The given equation is y=2x2-4. The general linear equation is of the form 

Q: b. Show all synthetic division work for credit. Express your answer in P(x)=D(x)Q(x)+R(x) notation. ...

A:

Q: Question #2

A: Observe that, in every table there are 4 values for x, and 4 values for y. In every case, the set of...

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A: Look at the figure based on the given information.

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A:

Q: 20 ) Solve the following rational equation: = 3 x+3 2/X

A:

Q: Find a possible formula for the exponential function through the points (−1,10) and (2,2/25 y= f(x)=

A: Let the exponential function is Since it passes through the points (−1,10) and (2,2/25)

Q: Write h(x) = | − 8 − 3x| as an equivalent piecewise-defined function.

A:

Q: 5. A population of bacteria decreases according to the following model: P(t)= 20(0.95) where P0) %3D...

A: (a) On January 1st the value of t = 0 days.Substitute  t = 0  in P (t) and find P (0).Hence, number ...

Q: The product of one more than a number and twice the reciprocal of the number is 12/5, find the numbe...

A: Let the number be n. By given condition, we have

Q: Consider g(x)=-3(1/5)x + 2 of the function f(x)=(1/5)x. Find the vertical intercept of g(x)

A:

Q: help

A:

Q: A  ship is travelling at 40 knots.  A train is travelling at 50 mph.  Convert the speeds.   ( 1 knot...

A: Ship travel at 40 knot and train travel at 50 mph.   Given that 1 knot=1.15 miles per hour.   To con...

Q: The hypotenuse of a right triangle is  13cm  long. The longer leg is  7cm  longer than the short...

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Q: For f(x)=x2+6 and g(x)=the square root of x-4 find the following composite functions and state their...

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Q: The length of a rectangle is  3 m  less than double the width, and the area of the rectangle is  ...

A:

Q: write the solution set in interval notation

A: Find the critical points of the inequality. We have the critical values x = 19, x = 20 and x = 21.

Q: Graph the function ?(?)=?2+2?−10f(x)=x2+2x−10by using completing the square to rewrite in vertex for...

A:

Q: As part of her retirement planning, Mrs. Campbell purchases an annuity that pays 5% compounded quart...

A:

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A: Let the time required to take by cold water faucet be “t”.   The hot water faucet twice as long to f...

Q: Two functions f and g are defined as in the attached picture.  Find the domain and the range of the ...

A: From the figure above we see that we do not have any value of (gof) for x=0,4,7 Because f of them is...

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Q: A recent advertisement claimed that 2 out of every 3 doctors recommended a certain herbal supplement...

A:

Q: NAME Lauren ferber STUDENT HANDOUT MATH 100 LAB 20 INSTRUCTOR ELDER For each of the following quadra...

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Q: The revenue and cost functions for a particular product are given below. The cost and revenue are gi...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Find the y-intercept for the graph of the quadratic function

A:

Q: Find and Simplify f (x+h) simplify your answer f(x)= -3x2-9x+6

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Q: Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through ...

A:

Q: The width of a rectangle is 3 less than twice its length. If the area of the rectangle is 70 cm", wh...

A: Let , length = x cm  So width = 2x-3 So area= x(2x-3) cm2  

Q: Find the equation of the line that has the given properties. Contains (-8, - 3), parallel to the lin...

A: Given, Points (-8, -3) and line y = -2x + 5

Q: Find x if:

A:

Q: A karat is measure of the purity of gold indicating how many parts out of 24 are pure.  Calculate th...

A: 16k gold means 16 parts of 24 are pure.   

Q: Suppose that a certain muffin shop has 240 ounces of dough and 280 ounces of sugar. It requires 4 ou...

A: Let's assume she makes S sugar cookies and C chocolate chip cookie

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A: Let the exponential function be It passes through (0, 3), therefore, we have

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.