Use the exponential decay model, upper a equals upper a 0 e superscript kt, to solve the following. the half-life of a certain substance is 19 years. how long will it take for a sample of this substance to decay to 78% of its original amount? it will take approximately nothing years for the sample of the substance to decay to 78% of its original amount.

It will take 7 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

Where,

= Initial amount of the substance,

If the half life of the substance is 19 years,

Then if t = 19, amount of the substance = ,

i.e.

Taking ln both sides,

Now, if the substance to decay to 78% of its original amount,

Then

Again taking ln both sides,

Hence, approximately the substance would be 78% of its initial value after 7 years.

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step-by-step explanation: