I'm working on a problem where I was given a table and had to find the exponential equation of best fit. The table is about the number of views of videos. The equation is y = 12.0143(1.7498)^x
I had to estimate the number of views after 2 weeks and that is 30,307 views.
The question then was, when will the video reach one million views. I'm not sure how to solve that? Do I make the y 1,000,000, so 1,000,000 = 12.0143(1.7498)^x?
If so, how do I solve that? If not, how to solve?
Thank you.
You are correct
12.0143(1.7498)^x=1000000
(1.7498)^x=83234
x log 1.7498 = log 83234
x = log83234/log1.7498 = 20.25 days
To solve the equation 1,000,000 = 12.0143(1.7498)^x for x, you are on the right track. The first step is to substitute 1,000,000 for y, which gives you:
1,000,000 = 12.0143(1.7498)^x
To isolate the exponential term (1.7498)^x, divide both sides of the equation by 12.0143:
(1,000,000 / 12.0143) = (1.7498)^x
Simplify the left side of the equation:
83,227.49 ≈ (1.7498)^x
Now, to solve for x, you need to take the logarithm of both sides of the equation. Since the base is 1.7498, you can use the logarithm with base 1.7498:
log base 1.7498 (83,227.49) = log base 1.7498 (1.7498)^x
The logarithm will cancel out the exponential term, resulting in:
x = log base 1.7498 (83,227.49)
Using a calculator or a software tool that can compute logarithms, calculate the logarithm with base 1.7498 of 83,227.49. This will give you the solution for x, which represents the number of weeks it would take for the video to reach one million views.
Note: Depending on the tool you are using, the notation for logarithms may vary. Some calculators or software use "log" to represent the natural logarithm (base e), while "ln" represents the base 10 logarithm. Make sure you choose the appropriate logarithmic function.