Question

You accidentally inhaled some mildly poisonous fumes. Twenty hours later, you see a doctor. From a blood sample, she measures a poison concentration of 0.00372 mg/cc, and tells you to come back in eight hours. On the second visit, she measures a concentration of 0.00219 mg/cc. Assume the concentration decreases exponentially.
a. Find an equation to model the situation.
b. Was the poison ever higher than 0.015 mg/cc ?
c. How long will it be when the poison concentration is just 0.00010 mg/cc?

Info so far:
(x,y) - (0,?) ; (20, 0.00372) ; (28, 0.00219)

Answer 1

equation: y=a(1-b)^x

Answer 2

actually its continuous, so y=ae^-b(x)

Answer 3

Let Ci = initial poison concentration and r = rate of decay
Then
\[0.00372=C _{i}e ^{-rt}.............(1)\]
and
\[0.00219=C _{i}e ^{-r28}...........(2)\]
Taking natural logs of both sides of equations (1) and (2) gives
ln 0.00372 = ln Ci - 20r .............(3)
and
ln 0.00219 = ln Ci - 28r .............(4)
Subtracting equation (4) from equation (3) gives
ln 0.00372 - ln 0.00219 = 28r - 20r ................(5)
Now you can solve equation to find r and then, by substitution, you can find Ci.

Answer 4

thanks!

Answer 5

You're welcome :) If you solve it please post your results.

Answer 6

working on it right now...

Answer 7

r = 0.00019125

Answer 8

I got r = 0.066228

Answer 9

yeah, r is actually 0.066228. I ended up doing elimination when you said subtract the equations.

Answer 10

ci is 0.0139

Answer 11

im done, thanks!

Answer 12

Good work!