An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 123 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.(a) Write an exponential function for the number of people A who had watched the video n hours after the initial observation. (Enter a mathematical expression.) A = 125(1.3)^n

For this case we know from the initial conditions that the value for a = 123 since is the starting value, so our model is given by:

Now we can use the other condition given "the number of people who had watched it was increasing by 30% every 3 hours", so for example after the first t =3 hours we will have a value for y = 1.3*123= 159.9, and using this condition we have this:

We can divide both sides by 123 and we got:

Now we can apply natural log on both sides and we have:

And our model for this case would be:

Step-by-step explanation:

For this case we want to construct and exponential model given by this general expression:

Where a is the initial amount and b the growth/decay constant.

For this case we know from the initial conditions that the value for a = 123 since is the starting value, so our model is given by:

Now we can use the other condition given "the number of people who had watched it was increasing by 30% every 3 hours", so for example after the first t =3 hours we will have a value for y = 1.3*123= 159.9, and using this condition we have this:

We can divide both sides by 123 and we got:

Now we can apply natural log on both sides and we have:

And our model for this case would be:

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