local fmt = require "fmt"

local function euler(f, y, step, finish)
    fmt.write(" Step %2d: ", step)
    for t = 0, finish, step do
        if t % 10 == 0 then fmt.write(" %7.3f", y) end
        y += step * f(y)
    end
    print()
end

local function analytic()
    io.write("    Time: ")
    for t = 0, 100, 10 do fmt.write(" %7d", t) end
    io.write("\nAnalytic: ")
    for t = 0, 100, 10 do
        fmt.write(" %7.3f", 20 + 80 * math.exp(-0.07 * t))
    end
    print()
end

local cooling = |temp| -> -0.07 * (temp - 20)

analytic()
for {2, 5, 10} as i do euler(cooling, 100, i, 100) end