SOLUTION: Any help with this homework question? Not sure of the formula. Thank you! "The amount of a sample of a radioactive substance remaining after t years is given by a function of th

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Any help with this homework question? Not sure of the formula. Thank you! "The amount of a sample of a radioactive substance remaining after t years is given by a function of th      Log On


   

Question 916506: Any help with this homework question? Not sure of the formula. Thank you!
"The amount of a sample of a radioactive substance remaining after t years is given by a function of the form Q(t) = Q0e^-0.0001t. At the end of 5,000 years, 50 grams of the substance remain. How many grams were present initially? Round your answer to the nearest hundredth gram."
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let f = q(t)
let p = q(0)

your equation becomes:
f=p*e^(-.0001*t)

replace f with 50 and t with 5000 to get:
50 = p*e^(-.0001*5000)

divide both sides of this equation by e^(-.0001*5000) to get:
50/e^(-.0001*5000) = p
use your calculator to solve for p to get:
p = 82.43606354 which you can round as desired.

confirm by replacing p with 82.43606354 in the original equation to get:
f = p*e^(-.0001*5000) becomes:
50 = 82.43606354*e^(-.0001*5000) which becomes:
50 = 50

this confirms the solution is good.