A new song has gone viral on the Internet. The website hosting the song uses the function f(t)=500t2
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 all work to receive full credit for this question.
We need to solve for t when f(t)=1,000,000.
500t^2 = 1,000,000
Divide both sides by 500:
t^2 = 2,000
Take the square root of both sides:
t = ±√2,000
Since time cannot be negative, we take the positive square root:
t ≈ 44.72
Therefore, the number of daily hits will reach 1,000,000 on approximately the 45th day.