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.
Can someone help me with this problem please and thank you?
Just in function f(t)=500 t² replace f(t) by 1,000,000
1,000,000 = 500 t²
Divide both sides by 500
2,000 = t²
t² = 2,000
t = √2,000 = 44.721
t ≈ 45 days
Remark:
≈ means almost equal to
is it correct?
To find the day on which the number of daily hits reaches 1,000,000, we need to solve the equation f(t) = 1,000,000 for t.
Given that f(t) = 500t^2, we can substitute it into the equation:
500t^2 = 1,000,000
To solve for t, divide both sides of the equation by 500:
t^2 = 1,000,000 / 500
t^2 = 2000
Now, take the square root of both sides:
√(t^2) = √2000
t = √2000
Using a calculator, we find that √2000 is approximately 44.72.
So, the predicted day on which the number of daily hits reaches 1,000,000 is approximately 44.72 days.
To find the day on which the number of daily hits reaches 1,000,000, we need to solve the equation f(t) = 1,000,000. In this case, the equation would be:
500t^2 = 1,000,000
To solve this equation, we will rearrange it and solve for t:
t^2 = 1,000,000 / 500
t^2 = 2000
Taking the square root of both sides:
t = √(2000)
t ≈ 44.7
Since time is measured in days, we can round up to the nearest whole number to get the predicted day on which the number of daily hits reaches 1,000,000. Therefore, the prediction is day 45.