Question

question 49 and then43

20-sec period after the booster rocket was activated. Hint: The distance is given by Jd 48. TABLET CoMPUTERS Annual sales (in millions of units) of a certain brand of tablet computers are expected to grow in accordance with the function f(r) = 0.13° + 0.16t + 2.64 6) (0 t 54· Cr per year, where t is measured in years, How many tablet computers will be sold over the next 6 years? in 49. CREDIT CARD DEBT The average U.S. household credit card debt stood at $8382 per household at the beginning of 2008 (t 0) and was changing at the rate of f) 2582 -680r 316(0SI4) dollars/year in year t from the beginning of 2008 until the 55. A beginning of 2012. What was the average U.S. household credit card debt at the beginning of 2012? Source: TIM. bi 50 US. NATIONAL DEBT The US national deht stood at 10 005

Answer 1

Let A(t) denotes the average U.S household credit card debt of any time 't' from 2008 where t = 0 corresponds to beginning of 2008. Also, it is given that rate of change of average U.S household credit card debit is given by f(t) = 258 t^2 - 680 t - 316 d/ddt A(t) = 258t^2 - 680t - 316 (Because Rate of change is also given by d/dt A(t) dA = (258t^2 - 680t - 316) dt Integrating both sides, we have integral dA = integral (258 t^2 - 680t - 316) dt A = 258 t^3/3 - 680 t^2/2 - 316t + c (because integral t^n dt = t^n + 1/n + 1 & integral dt = t) A(t) = 86t^3 - 340t^2 - 316t + C where C is constant of integration At t = 0 (beginning of 2008), A(t) 8382, we have from (*), 26(0)^3 - 340(0)^2 - 316(0) + c = 8382
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