To find: The quantity of mass that remains after 16days.
The quantity of mass that remains after 16days is .
The initial mass of the sample = 1g.
The half-life of Palladium-100 = 4 days.
Let the mass be m.
The initial mass = m and the mass of Palladium-100 in 4days = .
The mass after 8days=.
The mass after 12days= .
The mass after 16days=.
Since the initial mass m = 1g, the quantity of mass after 16 days is, .
Thus, the mass that remains after 16days is .
To find: The mass that remains after t days.
The mass that remains after t days is .
The initial mass of the sample=1g.
The half-life of Palladium-100 = 4days.
From part (a), the mass after 16 days is, .
The general form of the mass after n days is given by,
Therefore, the mass remains after t days is .
To find: The inverse of and explanation of its meaning.
The inverse of the function is and the meaning of the inverse function in which the time is passed when m gram is left.
Laws of logarithms:
If x and y are positive numbers, then
Let be the mass that remains after t days.
Then its inverse function is, .
Taking on both sides and simplify as follows.
Simplify further as,
Substitute t value in the equation (2)
Therefore, the inverse of the function is it represents the time when is passed when m grams left.
To find: When the mass is reduced to 0.01g.
The mass is reduced to 0.01g approximately in 26.6 days.
From part (a), .
Substitute in ,
Taking on both sides.
On further simplification,
Therefore, the mass is reduced to 0.01g approximately in 26.6 days.
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