If a quantity of substance decays exponentially, the following equation relates the amount of time t it takes for the substance to lose half its value to the decay rate k:
12Av0=Av0e^kt.
a. Solve the equation for t in terms of k.
b. What is the half-life of a substance whose decay rate is -7% per year?
Round your answer to the nearest tenth of a year.
c. Solve the equation for k in terms of t.
d. If the half-life of a substance is 7 years, find its decay rate. Round your answer to nearest tenth of a percent.

Question

If a quantity of substance decays exponentially, the following equation relates the amount of time t it takes for the substance to lose half its value to the decay rate k: 
12Av0=Av0e^kt.
a.  Solve the equation for t in terms of k.
b.  What is the half-life of a substance whose decay rate is -7% per year?
Round your answer to the nearest tenth of a year.
c.  Solve the equation for k in terms of t.
d.  If the half-life of a substance is 7 years, find its decay rate.  Round your answer to nearest tenth of a percent.

sherribelle · Answer

The 0 is a subscript of A, that's why the v's are there. They are not variables.

isaiah.feynman · Answer

You mean? $$12A_{0} = A_{0}e^{kt}$$:P

welshfella · Answer

As its decay i think that should be (1/2) A0   on left side

sherribelle · Answer

Yes, I apologize, 1/2Av0

isaiah.feynman · Answer

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