How can I do it?

Question

There were 273 mass shootings on day 302 of 2017. Assume there were 0 mass shootings on day 0.

If the linear trend continues, how many mass shootings will there be by day 365?

Answer 1

Oscar,

Scary world problems lead to scary word problems.

This word problem is just about finding the equation of a line and using that equation to find a specific point.

We could draw a line from day 0 with zero shootings to day 302 with 273 mass shootings. That is, we could draw a line from point (0,0) to point (302, 273). What is the slope of this line?

Use this little formula to find slope:

(0 - 273)/(0 - 302) = 0.9.

If this is the slope, the equation of our line is y = 0.9x (which means the number of mass shootings increase at a rate of 0.9 every day).

Plug in 365 to find that by day 365, we will have had y = 0.9(365) = 329 mass shootings.

Oh and why did we decide that the days is x and the number of mass shootings is y? It’s because we are trying to find the number of mass shootings as a function of time. Notice the obvious assumption that the number of mass shootings increases as time goes by. So number of mass shootings is a variable determined by time, just as y is a variable determined by x.

Hope this helps! :)

Answer 2

You will want to work with a linear function.

t = time in days

N(t) = number of mass shootings at time t

N₀ = initial number of shootings (i.e. at time t = 0)

N₀ = 0

r = linear rate of increase in mass shootings

N(t) = N₀ + rt

r = ΔN / Δt = (273 - 0) / (302 - 0) = 273/302

N(t) = 0 + (273/302)t = (273/302)t

At t = 365 days,

N(365) = (273/302) (365) = ?