Question

Please help with the following question and explain thoroughly. Thanks so much!

e profit, in millions of dollars, of a company t years after 1992 is given in the following table: t = # of years after 1992-10- 2-T-4-T6 Profit in millions of dollars 5 220 260 220 200 280 1. The 8-T-10 the number of years since 1992. Find the best model for P(t), the profit at time t, from the DRATIC, EXPONENTIAL, CUBIC or LOGISTIC. Give your model with (a) Let t be following choices: QUA four decimal places the rate of change of the profit t years (b) From after 1992. the model in part a), derive a function, P'(t), giving (o) According to the model, how fast was the profit changing in 2002? Show work. Give your answer rounded to two decimal places with units. (d) According to the model, what will the profit be in 2003? Show work. Give your answer rounded to two decimal places with units.

Answer 1

Answer: ---- Date: ----30/5/2019

P 1.93866t3-33.1647t165.301t+5.43651 R2 0.999 300 250 200 150 Poly. (P) 100 50 10 12 So we have the model as, P(t) 1.93866t33.1647t +165.301t +5.43651 (b.) We have, P(t).938663 33.1647t +165.301t 5.43651) dt P(t) 1.93866(3t2) 33.1647(2t)+165.301 P(t) 5.81598t2 -66.3294t165.301 which is the required rate of change of profit. (c.) The rate of change of profit in 2002 is, P (10) 5.81598(10)2 -66.3294(10) +165.301 P(10) 83.60 dollars per year (d.) P(t) 1.93866t3 33.1647t2 +165.301t5.43651 For t-11, P(11) 1.93866(113 -33.1647(11)2 165.301(11)5.43651 P(11) 391.18 So the profit in year 2013 is 391.18 dollars