Teacher's Guide - Pearson

d) 4 200 3 0.945 t < 1 000∴ t > 25.4∴ t 26 daysNote: Students should use the trial-and-error method. The inequality sign changesaround because the bases on either side of the equation are fractions. The followingexample may help students to understand it better:If (​1__2 ​)t < (​1__4 ​), then (​ 1__2 ​)t < (​1__2 ​)2 . This is possible only for t > 2.3. a) P 5 2 000 000 3 (1 1 ____ 1.9​100 ​)t5 2 3 10 6 3 1.019 tb) P 5 2 3 10 6 3 1.019 t 2 197 358 peoplec) 1.019 t 5 1.1∴ t 5.1 yearsProject (Student’s Book page 45)1. _____ 42 500 ​ 3 ____ ​ 1001 ​ 5 0.16% On the first day, this doesn’t seem much, but he should be concerned because theplant grows exponentially (the next day it covers double the surface area than theprevious day).2. It is exponential, because the growth doubles every day from the day before, notfrom the first day. A 5 4 3 2 t 2 1 , where t is the number of days starting from1 April. Alternatively,A 5 2 3 2 t 5 2 t 2 1 , where t is the number of days starting from 1 April.3.Surface area (m 2 )Number of days4. t 9.3 days (determined from the graph), so on 9 April it will cover half.5. t 10.3 days (determined from the graph), so on 10 April it will cover the damcompletely.6. Kill all the plants before 3 April, when it will still be manageable (16 m 2 ).Chapter 3: Indices15