Question

Application (12 marks) 7. An influenza virus is spreading through a school according to the function N(t) = 3(2), where N is the number of people infected and t is the time, in days. a) How many people have the virus initially, when t = 0? НА 12A b) Determine the average rate of change between i) day 1 and day 2 ii) day 2 and day 3 Compare the rates with respect to the given situation. 11A C) Estimate the instantaneous rate of change after 3 days. Explain what the value represents in this situation. IZA 8. a) Given the functions f(x) = x + 2 and g(x) = 3", determine an equation for (fog)(x) and (gºf)(x). 12A b) Determine f(g(3)) and g(f(3)). 12A c) Determine all values of x for which f(g(x)) = 9(f(x)). 12A Page 3

Answer 1

people at timet Number of infected Nit) 312)+ at teo N10) = 3(21° 3 the virus. Initially 3 people have Average rate of change is +(*) -f(x) ne a) day 1 and day 2. +12) - fil) 3(2) - 3(2) 2-) - 12-6 (ii) day 2 and day 3. 3(2)- 3(2) +13) - 42) 2-1 24-12 12 Average rate become double at the third day from the second day

instantaneous rate of change at time + dN dt. 2 3(2)+ dn at 3 (2) en (2) dN dt at t =3 dN at 1t=3 3(2)3 ln (2) 24 en (2) 24 X 0.6931 16.6355. instantaneous rate of change at t = 3 16.6355 at This. tells us the rate of change t=3 linstant) is. 16.6355. It b positive this shows that NA) es. growing very tast.