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The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 123 days and there is an amount equal to 150 grams now. What is the expression for the amount A(t) that remains after t days, and what is the amount of the substance remaining (rounded to the nearest tenth) after 365 days?

Hint: The exponential equation for half-life is A(t) = A0(0.5)t/H, where A(t) is the final amount remaining, A0 is the initial amount, t is time, and H is the half-life.

Respuesta :

Riia

Here we have to use the given formula of the half life which is

[tex] A(t) =A_{0} (0.5)^{t/h} [/tex]

A(t) is the amount remains after time,t, A0 is the initial amount and h represents the half life.

In the given question , initial amount is 150 grams, and half life is 123 days .

So the required expression is

[tex] A(t) = 150(0.5)^{t/123} [/tex]

In the second part, we have to find the amount remaining after 365 days.

So we put t=365 .

[tex] A(t) =150(0.5)^{365/123} = 19.18 grams . [/tex]

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