A radioactive material decays according to the function A(t) = Ao e^-.0244t where Ao, is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500 grams of the radioactive material (a) What is the decay rate of the radioactive material?
(b) Graph the function using a graphing utility. (c) How much radioactive material is left after 10 years?
(d) When will only 300 grams of the radioactive material be left?
(e) What is the half-life of the radioactive material?

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Step-by-step explanation:

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )