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.
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.
Solution
The function we're looking for is linear, because the number of words Nick writes is directly proportional to the amount of time he spends writing.
First, we need to find the rate at which Nick writes. We know that he writes 120 words in 30 minutes, so his rate is 120 words / 30 minutes = 4 words/minute.
This rate is the slope (m) of our linear function.
The y-intercept (b) of our function is the number of words Nick starts with at the beginning of his writing session, which is 500 words.
So, the equation for the function is f(x) = -4x + 500.
This function tells us how many words Nick still needs to write x minutes into one of his writing sessions. The negative sign indicates that the number of words he needs to write is decreasing over time.
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