Problem #4 Exponentials Math Refresher As we just noted, the \"x\" in e-x must b

Question

Problem #4 Exponentials Math Refresher As we just noted, the "x" in e-x must be dimensionless. A model process whose behavior is govemed by exponential behavior such as this is the decay of after some period of time t is given by: radioactive nuclei. Here, the number of remaining nuclei N Here, N(t 0) denotes radioactive decay (which has units of time). Note the number of radioactive nuclei present at t = 0, and denotes the "lifetime" of the then that the ratio t/t is dimensionless. If 100 s, calculate the time required for the Suppose number of nuclei to decrease by a factor of one-half. there are No radioactive nuclei present at t = o. NOTE: Answer: 69.3s

Explanation / Answer

given that n = n0/2

from the equation

n0/2 = n0*exp(-t/100)

exp(-t/100) = 1/2

exp(t/100) = 2

t/100 = ln(2) = 0.693

t = 100*0.693

t = 69.3 sec

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