contestada

A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few years. Write an equation representing the relationship, where \small x is time in years, and \small y is the number of songs available.

Respuesta :

facundo3141592

Answer: y = (3^(x-1))*1500

Step-by-step explanation:

We want the relationship

y = f(x)

where y is the number of songs, and x is the number of years.

We know that in the first year, x = 1, the site has 1,500 songs.

The next year, x = 2, the number of songs is tripled, then we will have:

1,500*3 = 4500 songs.

The next year, x = 3, we will have: 3*(3*1500) = (3^2)*1500.

when x = 4, the number is tripled again:

3*(3^2)*1500 = (3^3)*1500

We already can see the pattern, for the year x, the site will have:

y = (3^(x-1))*1500 songs.

This is the equation we are looking for.

The exponential equation that gives the number of songs available after x years is given by:

[tex]y(x) = 1500(3)^x[/tex]

What is an exponential equation?

It is modeled by:

[tex]y = ab^x[/tex]

In which:

  • a is the initial value.
  • b is the rate of change.

In this problem:

  • A new online music service has a collection of 1,500 songs, hence a  = 1500.
  • It expects to triple the number of songs each year for the next few years, hence b = 3.

Thus, the equation is:

[tex]y(x) = 1500(3)^x[/tex]

More can be learned about exponential equations at https://brainly.com/question/25537936

Otras preguntas