1) The radioactive element carbon- 14 has a half-life of 5750 years. If 100 gram

Question

1) The radioactive element carbon- 14 has a half-life of 5750 years. If 100 grams of this element are present initially how much will be left after 1000 years? 2) If $1000 is invested at 8% per year compounded continuously what will the investment be worth after 5 years? 3) The marginal cost function for a certain manufacturer is dC/dx = 25 + 20x = 0.03x^2 ( C = cost, x = units). It costs $2500 to produce 10 units. Find the production costs for 100 units. 4) Sketch: f(x) = (x-1)/(x+2) & list the asymptotes, critical #s, inflection points

Explanation / Answer

1) N =Noe^-kt k = ln2/5750 No = 100 gms t = 1000 N(t= 1000) = 88.6435 gms 2)(1000)(1.08)^5 = $1469.328 3)C= 25x + 10x^2 - 0.01x^3 +k x= 10 ; C = 2500 k = 2500 - 1240 = 1260 C(100) = $93670 4) x= -2 ---asymptote x=1 -- critical point

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