SOLUTION: How do I solve this growth and decay problem it reads: A material decays at a rate of 1.1% per year. If you start with 250 grams of the material, in how many years will there be 10

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I solve this growth and decay problem it reads: A material decays at a rate of 1.1% per year. If you start with 250 grams of the material, in how many years will there be 10      Log On


   

Question 706112: How do I solve this growth and decay problem it reads: A material decays at a rate of 1.1% per year. If you start with 250 grams of the material, in how many years will there be 100 grams remaining
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Every time period, the material lost 1.1% of what it had in the beginning of the period. Meaning that it becomes 100-1.1=98.9 percent of its strength as each time period passes.

Starting at any amount A, the first period makes A*0.989, the second time period means that there is A%2A0.989%2A0.989, and then for any number of time periods, the quantity remaining will be A%2A%280.989%29%5Et, where t is the number of time periods which pass.

If A%5B0%5D is the initial amount to start, the A%5Bt%5D is the amount remaining after t time. t can be in years, in this example.
A%5Bt%5D=A%5B0%5D%2A%280.989%29%5Et

If you want what t for starting with 250 grams and having 100 grams remaining,
100=250%2A0.989%5Et
2%2F5=0.989%5Et
ln%282%2F5%29=t%2Aln%280.989%29
t=%28ln%282%2F5%29%29%2F%28ln%280.989%29%29

Seems to be t=82.8 years or t=83 years.