Question

How do you differentiate `23000(0.93)^t`?

Answer 1

If you mean differentiate w.r.t `t`, firstly write it as :

• `z(t) = alpha beta^t, qquad {(alpha = 23000),(beta = 0.93):}`

Then maybe use log rules:

• `ln z = ln alpha + t ln beta`

Differentiate (?):

• `1/ z dz = 0 + dt * ln beta`

• `implies (dz)/(dt) = z * ln beta = alpha beta^t * ln beta`

This means that:

• `(dz)/(dt) = ln(0.93) * 23000 * 0.93^t`

A calculator kills that one stone dead.