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A new song has gone viral on the Internet. The website hosting the song uses the function f(t) = 2002t^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.

Respuesta :

After 22 days and 8 hours (0.349×24 hours) and 22 minutes (0.376×60 minutes) and 34 seconds (0.56×60 ≈ 34), the number of daily hits reaches 1,000,000.

It is given that the website hosting the song uses the function:

[tex]\rm f(t) = 2002t^2[/tex]    to represent the number of daily hits over time, where t is time in days.

It is required to predict the day on which the number of daily hits reaches 1,000,000.

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a function:

[tex]\rm f(t) = 2002t^2[/tex]

When f(t) = 1,000,000 then what will be the value of 't'

Simply:

[tex]\rm 1,000,000 = 2002t^2\\\rm 499.500 = t^2\\\rm \sqrt{499.500} = t\\\rm t = 22.349\ Days[/tex]

t = 22 days and 8 hours (0.349×24 hours) and 22 minutes (0.376×60 minutes) and 34 seconds (0.56×60 ≈ 34).

Thus, after 22 days and 8 hours (0.349×24 hours) and 22 minutes (0.376×60 minutes), and 34 seconds (0.56×60 ≈ 34), the number of daily hits reaches 1,000,000.

Learn more about the function here:

https://brainly.com/question/5245372

The day on which the number of daily hits of the considered song for the specified website reaches 1,000,000 is 23rd day.

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

So, suppose the day is t = d (dth day from the launch of the song) on which the daily hits reaches 1,000,000.

Then, evaluating the function [tex]f(t) = 2002(t^2)[/tex] at t = d should give us 1000000

Putting it, we get:

[tex]f(d) = 1000000\\2002(d^2) = 1000000\\\\\text{Dividing both the sides by 2002}\\\\d^2 = \dfrac{1000000}{2002}\\\\d = \sqrt{\dfrac{1000000}{2002}}\approx 22.35[/tex]

So after 22th day, ie on 23rd day (as 22.35 = 22 + 0.35 which shows 23rd day is still not completed) of the launch of the song, the number of daily hits reaches 1,000,000.

Thus, the day on which the number of daily hits of the considered song for the specified website reaches 1,000,000 is 23rd day.

Learn more about evaluating a function at a value  here:

https://brainly.com/question/2753269

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