Question

*Logarithmic Function*

A certain radioactive substance decays exponentially.The percent , P , of the substance left after , t, years is given by formula P(t)=100(1.04)^-t.Determine the instantaneous rate of decay of the substance when it has reached its half-life .

Answer 1

something wrong here
\[P(t)=100(1.04)^{-1}\] doesn't have a \(t\) in it

Answer 2

I'm sorry, i meant the power, -1 as the variable -t, thank you.

Answer 3

\[P(t)=100(1.04)^{-t}\] like this?

Answer 4

Yes, but I was able to solve it now, I had a mindlapse, sorry, you can confirm is the answer I got, t = 17.67 years is correct?

Answer 5

well you need two things, first the time when it is half, and then the instantaneous rate of change

Answer 6

first one you solve using logs
\[\frac{1}{2}=(1.04)^{-t}\]
\[t=-\frac{\ln(.5)}{\ln(1.04)}\]

Answer 7

which is t = 17.67, then find the derivative of the given equation?

Answer 8

yeah that looks right, 17.67

Answer 9

yeaaa, never mind, the question I had typed had a mistake

Answer 10

yes, and then replace \(t\) byu 17.67

Answer 11

But thanks so much, I'm going to close the question, thanks a lot ! fast answer and excellent help.

Answer 12

yw

Answer 13

after you get 17.67 how do u find it

Answer 14

i got I.R.O.C -0.4035

Answer 15

IS THAT THE ANSWER