Suppose strontium-90 decays at a rate of 2 percent per year.
(a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.)
Answer: P(t)=?
To determine the fraction P of strontium-90 remaining as a function of time, we need to take into account the decay rate of 2 percent per year.
The decay rate of 2 percent per year means that after one year, 2 percent of the strontium-90 will decay, leaving 98 percent remaining. Thus, we can say that after one year, P(1) = 0.98 or 98 percent remaining.
In general, we can write the fraction P as a function of time t using the formula:
P(t) = (1 - r)^t
where r is the decay rate expressed as a decimal (in this case, 2 percent or 0.02) and t is the time measured in years.
Therefore, for the given situation:
P(t) = (1 - 0.02)^t
Simplifying further:
P(t) = 0.98^t
This is the function that describes the fraction P of strontium-90 remaining as a function of time t, measured in years.