Calculus
posted by lala .
A certain radioactive material decays exponetially. The percent, P, of the material left after t years is given by P(t)= 100(1.2)^t
a)Determine the half life of the substance

From the equation we can see that the original amount was 100 units
So we want to know when that amount becomes 50
50 = 100(1.2)^t
.5 = 1.2^t
log(.5)= log(1.2^t)
log(.5)= tlog(1.2)
t = log(.5)/log(1.2)
= 3.8
so t = 3.8 years is the halflife time
Respond to this Question
Similar Questions

Physical Science
A gram of radioactive material has a halflife of one year. After four years how much radioactive material will be left...0g, 1/2g, or 1/4g? 
physical science
A certain radioactive substance has a halflife of 1 hour. If you start with 1 gram of the material at noon, how much will be left at 3:00 P.M.? 
Science
Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(t). a) Determine the function A’, which represent the rate of decay of the substance. b) … 
calculus
The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100gram sample … 
College Algebra
The halflife of a radioactive material is about 34.6 years. How much of a 1gram sample of the material is left after 30 years? 
Algebra 2 help...
A half life of a certain radioactive is 36 days. An initial amount of the material has a mass of 487 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. … 
algebra
A radioactive substance decays according to the formula A=A0e^kt where A0 is the initial amount of substance (in grams) A is the amount of substance(in grams) after t years k is a constant The halflife of the substance is 10 years.If … 
Calculus
The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = .022m, where m is the mass of the isotope in mg and t is the … 
math
6. The halflife of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains … 
Math
A radioactive material has a half life of 500 years. A) Given 20 grams of this material, how much will remain after 1,000 years?