another weird math question?

Question

the % P of physicians using a new medication after t months is given by P(t) = 100% (1-e^-.2t)

I need to find out what percentage of physicians are using the medication after 1 month, and the rate of change P'(t)

can anyone help

Answer 1

t = 1 month, and plug in the value of t = 1

P (t) = 100 (1 - e^-.2) = 100 (1 - .8183) = 18.17%

dP/dt
= 100 d/dt(1 - e^-.2t)
= 100 x [0 - e^(-.2t) x (-.2)]
= 100 x .2 x e^(-.2t)
= 20 e^(-.2t)

Answer 2

Substitute 1 for t into the equation; obtain your results from any handy calculator.

To find P'(x), just take the derivative of P(x). g'(e^f(x)) = e^f(x) * f'(x).