help me solve this problem?

Question

suppose that when a particular drug is injected, the concentration is 1.5mg/mL. After 4 hours, the concentration has dropped to 0.25mg/mL. Solve for the decay constant, k, and write an exponential decay equation. How long would it take for the concentration to drop to 0.10mg/mL?

Answer 1

y=Ce^kt

 

the Initial is the C.  The final is the y.  t = 4

 

.25=1.5e^4k

 

Divide .25 by 1.5 to get .167

 

So we do this now

 

.167=e^4k

 

Take a natural log of both sides to get

 

ln(.167=ln(e^4k).  ln and e cancel each other out since they are inverses of each other therefore the equation would look like this:

 

ln(.167)=4k.  Divide by 4 to solve for k.  This is your rate constant.  ln of .167 = -1.789761.  You would divide this answer by 4 to get teh k. k= -.447

 

This is telling you that it is decaying.

 

Since you have k.  You can now solve for the time it takes for this to get to .10. 

 

.10=1.5e^-.447t

 

Follow the same steps. Divide .10 by 1.5.  take ln of both sides then divide by -.447. You will have your answer.  Thanks