SOLUTION: Cesium-142 has a half life of 50 years. If there are 20 grams now: a. Fill in the equation y=ab^x b. Find the growth factor (b) for this exponential function

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Cesium-142 has a half life of 50 years. If there are 20 grams now: a. Fill in the equation y=ab^x b. Find the growth factor (b) for this exponential function      Log On


   

Question 1010625: Cesium-142 has a half life of 50 years. If there are 20 grams now:
a. Fill in the equation y=ab^x
b. Find the growth factor (b) for this exponential function
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You have only one datum point in the half-life information, and then a value for making a question. Why not the basic exponential decay equation like y=pe%5E%28-kt%29?

Try your simpler format anyway.
Half-life information would seem to make %281%2F2%29=1%2Ab%5E50, using a for the initial quantity of Cs-142.

b%5E50=1%2F2

log%2810%2C%28b%5E50%29%29=log%2810%2C%281%2F2%29%29

50%2Alog%2810%2Cb%29=log%2810%2C%281%2F2%29%29

log%2810%2Cb%29=%281%2F50%29log%2810%2C%281%2F2%29%29

log%2810%2Cb%29=-0.0060206

....
highlight%28b=0.986%29
The model being highlight%28y=a%280.986%29%5Ex%29, using a as the initial quantity.
This b value is not a growth factor!! The "growth" is negative, not positive.

Having "twenty grams now", you can write y=20%280.985%29%5Ex.