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.

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.

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.