The equation M(t)=19e^(−t/43) describes the amount of radioactive isotopes as a function of the time

Question

The equation M(t)=19e^(-t/43) describes the number of radioactive isotopes as a function of the time t(years). After how much time has the amount decreased to 1/6 of the original amount? The answer shall be written as t=a ln b where a and b are whole numbers and a is not equal to 1

Answer 1

M(t)  = 19e^-t/43

 

Original amount = M(0) = 19

 

Find t so that M(t) = 19/6:

 

    19e^-t/43 = 19/6

 

        e^-t/43 = 1/6

 

    ln(e^-t/43) = ln(1/6)

 

          -t/43 = ln(1) - ln6

 

          -t/43 = -ln6

 

               t = 43ln6 ≈ 77 years