The growth function per hour is f(x) = 5500(1.65)ˣ
To find the growth rate per hour, we should find the derivative of f(x). Take the natural log of the equation. ln(f) = ln[5500(1.65)ˣ] = ln(5500) + x ln(1.65)
Take the derivative with respect to x. f'/f = ln(1.65) = 0.5 Therefore the derivative is f' = 0.5f = 2750(1.65)ˣ = 275000(1.65)ˣ percent or 2.75 x 10⁵ (1.65)ˣ percent