SOLUTION: Use the given information to find an exponential model of the form Q = Q0e−kt or Q = Q0ekt, as appropriate. Round all numerical values to three significant digits when rounding i

Algebra ->  Exponents -> SOLUTION: Use the given information to find an exponential model of the form Q = Q0e−kt or Q = Q0ekt, as appropriate. Round all numerical values to three significant digits when rounding i      Log On


   

Question 1190860: Use the given information to find an exponential model of the form Q = Q0e−kt or Q = Q0ekt, as appropriate. Round all numerical values to three significant digits when rounding is necessary.
Q is the amount of radioactive substance with a half-life of 160 years in a sample originally containing 7 grams (t is time in years).
Q =
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Q%5B0%5D+=+7 is the original amount in grams.

We'll use the exponential decay model Q+=+Q%5B0%5De%5E%28-kt%29.
The negative exponent is what causes the decay.

The half-life is 160 years, which means at time t = 160, the initial amount is cut in half to 7/2 = 3.5 grams
Plugging t = 160 leads to Q = 3.5

This is sufficient to help us find k
Q+=+Q%5B0%5De%5E%28-kt%29

3.5+=+7e%5E%28-k%2A160%29

3.5%2F7+=+e%5E%28-160k%29

0.5+=+e%5E%28-160k%29

ln%280.5%29+=+-160k

k+=+-ln%280.5%29%2F160

k+=+0.0043321698785 which is approximate

k+=+0.00433 when rounding to 3 sig figs. The three zeros aren't significant figures.

Answer: Q+=+7e%5E%28-0.00433t%29