Question

Nick wants to be a writer when he graduates, so he commits to writing 500 words a day to practice. It typically takes him 30 minutes to write 120 words. You can use a function to approximate the number of words he still needs to write x minutes into one of his writing sessions.

Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.

Answer 1

AI-generated answer

To find the equation for the number of words Nick still needs to write x minutes into one of his writing sessions, we need to consider the rate at which he writes and the total number of words he aims to write.

We know that Nick commits to writing 500 words a day, which means he writes 500 words in 24 hours or 1440 minutes (since there are 60 minutes in an hour). This gives us a rate of 500 words / 1440 minutes = 0.347 words per minute (rounded to three decimal places).

Now, we can set up the equation for the number of words Nick still needs to write x minutes into his writing session, let's call it f(x).

Since the rate of writing is constant, the equation is linear. Therefore, we can write it in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (m) represents the rate of writing, which is 0.347 words per minute. The y-intercept (b) represents the initial number of words Nick needs to write at the beginning of his writing session, which is 500 words.

Therefore, the equation for the function is:

f(x) = 0.347x + 500

This equation gives the number of words Nick still needs to write x minutes into one of his writing sessions.