Question

1. The number of people infected by a disease is being studied. Starting with a single patient, the number infected was shown to double every 5 days. Prove that the function N(t) = 24 can be used to model this behavior, in t days. N(0)= N(5)= N(10) N(15)= 2. Now, suppose the number infected doubles every 4 days. Which of these functions can be used to model N(t)? a) N(t) = 24 NO N(4)= N(8)= b) N(t) = 21/4+ N(0) N(4)= N(8)=

Answer 1

The given question is solved using the concept of growth and decay:

at Let the function be al(t)= Aol, where to is initial quantity/ No. Given (Ao all && is constant. : n(A)= est o

① ts day a(t) = 2 a linnast i Nct. (142) € x 15 ) e. No= 221 Nes) a 2 =2 N(10) = 2:4 N(15) = 2328 t = 4 days, N(4+4)= 2N (t) as I n(t) = q At N(O)= 2-1 N (4) = 216 N18 = 232 Hence, every t- 4 days Nct becomes 2 26 fins ocas is wrong.

lat b) Nlta 2 Ncos: 2 I not dowdays N(4) 2 1 (8) = 2432 . (b) is won Not doubling every 4 days (6) is wrong. N18) - correct Aus: [244]. Nees

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