Question

AABE * A-D- A- Emphasis АавbC АавbCсC AaBbccЕ Аа Heading 1 1 Normal Strong nt IS Paragraph Styles 2. The growth in the number of employees of a company can be described by the equation: NO)- 275(0.55)0.45 t in years a. How many employees will the company have after 4 year (t = 4)? b. What is the maximum number of employees you would expect this company to have if the growth follows this Gompertz curve? (Hint: Graph the function N(t) I Display Settings D Focus ORI e CH E O: 0 인 F6 F7 FB FO F10 F11 000 F12 $ % & 7 a

Answer 1

al N(A) 275 (0.55) (0.55) (0.45 jet .. No. of employees after t= 4 years = N(4) 275 (0.55) (0.45)4 268.34 268 ans There will be 268 employees in company after 4 years. (6) We x We want to find maxinnum value of N(X) know graph of is strictly decreasing for (where oca<1) ya y=ax (ocac1) - Max. value is at xo (645) is an a= .55 (i) Take then (55) increasing function, and has max. value when 6u5lt It is possible at too CS Scanned with CamScanner

Now Lim N) Lim to 295 (155) (045)* too 275 (:55) 275 (1) Max. possible value of N(A) 1275 employees ans. as .45 0 Note : t (i.) (645) is always zo (ii) Gompertz curve : y , x CS Scanned with CamScanner