Modeling Linear Equations

Question

Makayla is reading a 400-page book for her book club. She reads 32 pages each hour.Construct a function that models the number of pages, 𝑃, Makayla has left to read after 𝑡 hours of reading.

Answer 1

A linear function then, something that may look like "y = mx + b". So, we want to model number of pages left as a function of time.

We have a 400 page book for starters, so at time 0 we should equal 400. This tells us our y-intercept "b"! It is 400 here because of what we previously said.

Then, we know that Makayla reads 32 pages per hour. This sort of statement ("something" per time) implies the slope "m" of our function! It is actually "-32" in this case, because we are modeling pages remaining, and that is decreasing with time (fewer and fewer pages left!)

So we wind up with something like P(t) = -32t + 400 or P(t) = 400 - 32t ; pages left equals 400 pages to start minus 32 pages per hour, times however many hours she has been reading.

We can sanity check ourselves and plug in 0, and we get 400, which we want. *spoilers ahead* We can even solve for when there are no pages left (she finished!) That would be 0 = -32t + 400, t = 32.5 hours to finish the whole book.