How do you find the associated exponential decay or growth model: Q = 1,500 when t = 0; half-life = 1?

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Answer 1 · 2017-05-20T19:44:36

Start with #Q(t) = Q(0)e^(lambdat)#
Use the fact that #(Q(t_"half-life"))/(Q(0)) = 1/2# to find #lambda#

Start with #Q(t) = Q(0)e^(lambdat)" [1]"#

At #t_"half-life" = 1#

#(Q(1))/(Q(0)) = 1/2 = e^(lambda(1))#

Use the natural logarithm on both sides:

#ln(1/2) = ln(e^(lambda(1)))#

Flip the equation:

#lambda = ln(1/2)#

This is a better form:

#lambda = -ln(2)#

Substitute #1500# for #Q(0)# and #-ln(2)# for #lambda# into equation [1]:

#Q(t) = 1500e^(-ln(2)t)#