A new song has gone viral on the Internet. The website hosting the song uses the function \large f\left(t\right)=200t^2 to represent the number of daily hits over time, where t is time in days. Use the function to predict the day on which the number of daily hits reaches 1,000,000. Show your work.
To predict the day on which the number of daily hits reaches 1,000,000, we need to solve the equation f(t) = 1,000,000.
Given that f(t) = 200t^2, we can substitute this expression into the equation:
200t^2 = 1,000,000.
Now, we can solve this equation for t:
200t^2 = 1,000,000
Divide both sides by 200:
t^2 = 1,000,000 / 200
t^2 = 5,000
Take the square root of both sides to solve for t:
t = √5,000
t ≈ 70.71
Therefore, the number of daily hits is predicted to reach 1,000,000 on approximately the 71st day.
To predict the day on which the number of daily hits reaches 1,000,000, we can set up an equation using the given function and solve for the value of t.
The equation is: f(t) = 1,000,000.
Substituting the given function into the equation, we have: 200t^2 = 1,000,000.
To solve this equation, we need to isolate the variable t.
Divide both sides of the equation by 200: t^2 = 5,000.
Taking the square root of both sides of the equation, we have: t = sqrt(5,000).
Using a calculator, we find that the square root of 5,000 is approximately 70.71.
Therefore, the number of daily hits reaches 1,000,000 on approximately the 71st day.
Note: It is important to remember that this is a predicted value based on the given function and assumes that the function accurately represents the actual number of daily hits over time. In reality, various factors can influence the actual number of hits, so this prediction should be taken as an estimation.