Question

FSTM3074 MATHEMATICS FOR SCIENTISTS CHAPTER 2 - EXPONENTIAL AND LOGARITHMIC 14. The population of a colony of mice is approximately modelled by P, = 2.3e0:24 after 6 months. a) Draw a graph of P, against t for 0 3 1 3 15. b) Draw a graph of In P against i for 05 1 < 15. c) Estimate from either graph in (a) or (b), the population of mice after 7 months. d) Which of the two graphs is easier to use?

Answer 1

Sois Population mice modelled by = 2.36 po.at t + months a Graph of P4, 04t215 0.2+ P = 2:30 ezt we It has le exponential function and know that exponential fonction is Smooth and when Value of t increases it increases and when t decreases it decexeases P: cofficient of t is positive) By mutiplying positive no 2:3, basic nature ( discused above) cf remains Same e0.2€ Also, at t=0, 2-3 on this Basis we can draw OUZ graph now. t increases gxoph increases + deseases geap decreases -2.3 2 4 6 8 10 12 14 16 t 7 62 0.2t 2.3 e > PL - dm (Pt) = m [(2:3)|e®zt ) ] = JN (2:3) + um (eo:zt) ► ylt) = m (Pt) = ln (2:3) + o.zt im (e) = In (Pt) = dn (2.3) +0.2t t)

> where Equation is form: y=mt + c m=0.2 c = In (2.3) Equation of yd) = un ) is a straight line, with y intercept -cjm (2:3) - 0.83 e tc int except when i.e. Jn (2.3) to 2t=0 t - - Un (2:3) 0.2 = -4.16 y=0 .. we get two points: 0,0-83) 4 (-4-16,0) Now, we can draw OUX graph. Y(t) = n(P) +- 2.23 0-23 -4 -2 1 1 u z 3 5 6 7 t ? You on paper it gives - Using gooph (b) we can easily find population of mice after 7 month. plot graph by above method graph then perfect answeo As I am not using graph paper So I manually Calcutod After t-7 month population of mice : y(t)= In (A) = 14(2-3)+02 9(t) = 2.23 .. Use as it is Graph (C) is easies d) off course stoaight line