Question

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.

Answer 1

Answer:

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:

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