Question

9. The rate of change of y is proportional to y. A given business is losing market, therefore the monthly sales are plunging exponentially. At month 3 the sales were 4 (million) dollars.. At month 5 the sales were 1 (million) dollars. How much were the sales at month 02 hint: it is obvious that at month zero the sales were greater than 4 million dollars, 10. This follows the logistic model. Mr. ZeMarcelino put 10 animals on his farm to let them grow on their own (assuming all variables favor such endeavor). The animal growth follows the Logistic Equation, with b-60 and k-0.55 and a carrying capacity of 100 animals. Given the information above. show all work to answer: a) at what time (where t is in years) will the number of animals reach half the carrying capacity? b) at what time will Mr. ZeMarcelino have 80 animals? (keep the time to 2 decimals).

Answer 1

of chnge of is given teot 9cate 1he we Core to u's that tantinualy Lose in mwyket the ge and also a Sign uindicates t whou K s tonstont ard decay maiket un he gides eunth both espect to t get dt ln (ty) -Kt +c el's e ehon Constants -KHC Ge tRat 4million d&llars million dollas ues ton also t-3months we as at at ta5 morhs 1 and ing thes will fiud valus C and k. ue 3K and 3K+GK +2K

0.693142 K Now in 1-Gesk K=O-69314 =Ge 1- 0.03125G 32-G -3.4657 -O-693144L 22 e 40 cales at month 3 2