Question

The Screaming Salamanders, a new rock band, released their new music video early for subscribers of their fan page. When the video was released to the public, it already had 2,642 views. One day later, the number of views increased to 3,963, and the band expects that the number of views will continue to grow each day. Write an exponential equation in the form y=a(b)x that can model the total number of views, y, x days after the music video was released to the public. Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answer 1

The exponential equation to model the growth in views of The Screaming Salamanders' music video, using the form y=a(b)^x, is y=2,642(1.5)^x. This is based on the initial value of 2,642 views, with a growth factor of 1.5 each day after the release.

Step-by-step explanation:

To model the exponential growth of the music video views for The Screaming Salamanders, we can use the given data to determine the base growth rate and the initial value. Let's take y as the number of views, x as the number of days after the release to the public, a as the initial number of views, and b as the growth rate per day. On the day of the release, we have 2,642 views, and one day later, we have 3,963 views.

First, we recognize that a is the initial amount of views, which is 2,642. To find b, the growth rate, we divide the number of views on the second day by the number of views on the first day:

b = 3,963 / 2,642 = 1.5 (rounded to the nearest tenth)

Therefore, our exponential equation modeling the total number of views, y, x days after the release to the public is:

y = 2,642(1.5)x

Note that because we want to use whole numbers, decimals, or simplified fractions, we rounded the value of b to 1.5 which is an approximation for the sake of simplicity.