The amount of a radioactive substance decreases by 10% every 12 hours. Currently the amount of substance is 100 grams. If n is a whole number, which expression represents the number of grams of substance left n days from now? Select one:highlight_offhighlight_offhighlight_off
Question
The amount of a radioactive substance decreases by 10% every 12 hours. Currently the amount of substance is 100 grams. If n is a whole number, which expression represents the number of grams of substance left n days from now? Select one:highlight_offhighlight_offhighlight_off
Solution
The radioactive substance decreases by 10% every 12 hours. This means it decreases by 10% twice a day (since there are 24 hours in a day).
The formula for exponential decay is A = P(1 - r)^nt, where:
- A is the amount of substance left after time t
- P is the initial amount of the substance
- r is the rate of decay
- n is the number of times the substance decays per time period
- t is the time period
In this case:
- P = 100 grams (the initial amount of the substance)
- r = 10% or 0.10 (the rate of decay)
- n = 2 (since the substance decays twice a day)
- t = n days (the time period)
So, the expression that represents the number of grams of substance left n days from now is:
A = 100(1 - 0.10)^2n
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