Question

Previous Problem List Next Results for this submission Entered Answer Preview Result 375504.8234 375504.8234 -4069.019 -4069.019 ncorrect At least one of the answers above is NOT correct. (1 point) An investment portfolio changes value at the rate V') 103 whre V is in thousands of doilars and t is the number of years after 2004. By how much does the value of the portfolio change between the years: a. 2004 and 2008? ANSWER:375504.8234 b. 2008 and 2010? ANSWER:-4069.019 Note: You can eam partial credit on this problem. Preview My Answers Submit Answers Your score was recorded.

Answer 1

Given differentially equation is v^(t) = 10e^-0.06t (e^0.2t - 3) dv/dt = 10e^(0.2 - 0.06)t - 30e^-0.06t now we will do integration where t will vary from 0 to 4 for the year 2004 to 2008 (as initial value is 2004 considering were 0) so, integral^2_0 dv = 10intgeral^4_0 e^0.14t dt - 30integral^4_0 e^-0.06t dt v = 10/0.14 [e^0.14t]^4_0 + 30/0.06 [e^-0.06t]^4_0 = 10/0.14(1.7506725 - 1) + 30/0.06(0.78662786 - 1) = 53.61946429 - 106.68607 = -53.06660571 so, 53.06660571 number of port folio has been decreased from 2004 to 2008 For the year 2008 to 2010 to we have intwegral^2_0 dx = 10integral^2_0 e^0.14dt - 30 integral^2_0 e^-0.06t dt v = 10/0.14 [e^(22 times 0.14) -1] + 30/0.06[e^-0.06 times 2) - 1] = 23.08070088 - 56.53978164 = -33.45908076 so, 33.4908076 thousands of dollars portfolio has been decreased from 2008 to 2010