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Posted by on Tuesday, December 1, 2009 at 9:16pm.

The half-life of sodium-24 is 14.9 hours. A hospital buys a 40 mg sample of sodium-24.
a) How many grams, to the nearest tenth, of sodium-21 will remain after 48 h?
b) After how long will only 2.5 mg remain?

I don't know how to write the exponential function in order to be able to solve this. ><

  • MATH - solving exponential equations - , Tuesday, December 1, 2009 at 10:28pm

    amount = 40(1/2)^(t/14.9) , where t is the number of hours.

    test: if t = 0, Amount = 40 , Check!
    if t = 14.9
    amount = 40(1/2)^1 = 20 , Check!


    a) if t = 48
    Amount = 40(1/2)^(48/14.9)
    = 40(1/2)^3.22147651
    = 40(.107210899)
    = appr. 4.29 g

    b) 2.5 = 40(1/2)^(t/14.9)
    .0625 = (.5)^(t/14.9)
    t/14.9 = ln.0625/ln.5
    t/14.9 = 4
    t = 4(14.9) = 59.6 hours

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