A population of bacteria can be modeled by the function f (t) = 400 (0.98) t, where t is time in hours. What is the rate of change in the function?

the rate of change is f' (t) = (-8.08) * (0.98^t)

Step-by-step explanation:

If the function is

f (t) = 400 * (0.98) ^t

then the rate of change of f (t), that is f' (t) = df (t) / dt is

f' (t) = 400 * d (0.98^t) / dt

since the derivative of a function of the type g (x) = a^x is g' (x) = ln (a) * a^x, then

f' (t) = 400 * d (0.98^t) / dt = 400*ln (0.98) * (0.98^t)

f' (t) = (-8.08) * (0.98^t)