The half-life of palladium-100, 100pd, is four days. (so half of any given quantity of 100pd will disintegrate in four days.) the initial mass of a sample is one gram. (a) find the mass that remains after 16 days. (b) find the mass m (t) that remains after t days. (c) find the inverse of this function and explain its meaning. (d) when will the mass be reduced to 0.01 g?

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Mathematics

Kennedy Barber

7 June, 13:09

The half-life of palladium-100, 100pd, is four days. (so half of any given quantity of 100pd will disintegrate in four days.) the initial mass of a sample is one gram. (a) find the mass that remains after 16 days. (b) find the mass m (t) that remains after t days. (c) find the inverse of this function and explain its meaning. (d) when will the mass be reduced to 0.01 g?

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Brennen Wallace · Answer 1

First the formula of Remaining palladium is y=1 * (1/2) ^n

1 shows at first we have 1 gr of palladium

a) y=1 * (1/2) ^4=1/16

b) the mass m (t) that remains after t days is y = (1/2) ^ (t/4)

t=-4 log2 (y)

we can find time using this

d) t=-4 log 2 (0.01) = (-4) * (-6.67) = 26.6