Question 1148014: The radioactive tracer ⁵¹Cr can be used to locate the position of the placenta in a pregnant woman. Often the tracer must be ordered from a medical laboratory. If A₀ units (microcuries) are shipped, then because of the radioactive decay, the number of units A(t) present after t days is given by
A(t) = A₀e^(−0.0249t)
a) If 40 units are shipped and it takes 2 days for the tracer to arrive, approximately how many units will be available for the test? (Round your answer to one decimal place.)
units
(b) If 40 units are needed for the test, approximately how many units should be shipped?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is A[t] = A[0] * e ^ (-.0249 * t)
when t = 2, the formula becomes A[2] = A[0] * e ^ (-.0249 * 2)
this results in A[2] = 38.05678758.
if A[2] is required to be 40, then the formula becomes 40 = A[0] * e ^ (-.0249 * 2)
solve for A[0] to get A[0] = 40 / e ^ (-.0249 * 2) = 42.04243453
to have 40 units available in 2 days, 42.04243453 units would need to be shipped.
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