The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. How do you write an exponential function that models the decay of this material and how much radioactive material remains after 10 days?

1 Answer
Jul 18, 2016

Let
#m_0="Initial mass"=801kg " at "t=0#

#m(t)="Mass at time t"#

#"The exponential function",m(t)=m_0*e^(kt)...(1)#
#"where " k=" constant"#

#"Half life"=85days=>m(85)=m_0/2#

Now when t =85days then

#m(85)=m_0*e^(85k)#

#=>m_0/2=m_0*e^(85k)#

#=>e^k=(1/2)^(1/85)=2^(-1/85)#

Putting the value of #m_0 and e^k# in (1) we get

#m(t)=801*2^(-t/85)# This is the function.which can also be written in exponential form as

#m(t)=801*e^(-(tlog2)/85)#

Now the amount of radioactive material remains after 10 days will be

#m(10)=801*2^(-10/85)kg=738.3kg#