Mathematics, 22.04.2020 19:53 eaves001

During this same time, the digital print manager tracked the number of visits to the website’s homepage. He found that before launching the new marketing plan, there were 4,800 visits. Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.

Write an equation to model the relationship between the number of weeks, x, and the number of site visits, f(x).

Enter the correct answer in the box by replacing the values of a and b.

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Answer from: fiorentinologan4

The relationship between the number of weeks, x, and the number of site visits, f(x) is:

$f(x)=4,800e^{0.081x}$

a: 4800

b=0.081

Step-by-step explanation:

We have a model for f(x): number of visits, in function of x: number of weeks since launch.

We consider a constant rate of increase, so we can write the model as:

$\dfrac{dy}{dx}=ay$

The solution to that differential equation is:

$y=ae^{bx}$

We know that the initial condition is y(0)=4800, so the equation becomes:

$y(0)=ae^{b*0}=4800\\\\a=4800$

We also know that at the fift week (x=5), the amount of visits is 1.5 times the initial number:

$\frac{y(5)}{y(0)}=e^{b(5-0)}=1.5\\\\5b=ln(1.5)\\\\b=ln(1.5)/5=0.081$

Then, the relationship between the number of weeks, x, and the number of site visits, f(x) is:

$f(x)=4,800e^{0.081x}$

Answer from: Quest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Answer from: Quest

Your answer should be 1/3. i hope i could ! good luck : )

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