# calculus

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The half-life of the radioactive isotope gallium-70 is 20 minutes. If the initial amount of gallium-70 is 25 milligrams, when will 10 milligrams be left?

• calculus -

can you solve

10 = 25(.5)^(t/20) where t will be in minutes ?

• calculus -

This is what I got..

25(1/2)^(t/20)=10
(1/2)^(t/20)=10/25=2/5

(1/2)^(t/20)=2/5
t/20=log(2/5)/log(1/2)
t=20(log(2/5)/log(1/2))
t=26.44

Is this correct?

• calculus -

correct, good job.

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