In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.
Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e-0.05tInitially, M0= 300e0=300 x 1 = 300When the substance mass has decreased to half its initial value, M = 0.5 x 300 = 150.Hence, we have the equation 300e-0.05t= 150Solve: e-0.05t= 0.5-0.05t= ln 0.5t = -20ln0.5= 13.8629...= 13.9 (3 s.f.)It will take 13.9 minutes for the substance mass to decrease to half its original value.
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