Given is the formula:

N (t) = 150 (1 - e^-0,05t)

The derivative is:

N' (t) = 7,5e^-0,05t

Explain how to get from the first formula to the second one.

Step-by-step explanation:

N (t) = 150 (1 - e^ (-0.05t))

First, distribute:

N (t) = 150 - 150 e^ (-0.05t)

Now, take the derivative. Recall that the derivative of e^u is e^u du.

N' (t) = 0 - 150 e^ (-0.05t) (-0.05)

N' (t) = 7.5 e^ (-0.05t)