Teacher's Guide - Pearson

Activity 3.3 (Student’s Book page 43)1. The size of the flea population doubles every five days. Therefore, the exponentshould be expressed as a multiple of 5.2. 240 fleas3. 20 daysActivity 3.4 (Student’s Book page 44)1. Growth 5 P10 000 1 P10 000 3 ____ 14.5​100 ​5 P10 000(1 1 0.145)5 P10 000 3 1.145∴ Penny’s money is multiplied by 1.145 each year.2. P10 0003. a) A 5 P10 000 3 1.145 25 P13 110.25b) A 5 P10 000 5 1.145 55 P19 680.11c) A 5 P10 000 5 1.145 105 P38 730.664. No, the investment’s value after 5 years is P19 680.11. Therefore, the investmentwill double in the 6 th year.5. P10 000 3 1.145 n 5 P338 000∴ 1.145 n 5 33.8∴ n 26 yearsExercise 3.3 (Student’s Book page 44)1. a) The number of bacteria in the culture doubles every minute.b) 180 bacteriac) t 0 1 2 3 4 5N 5 180 3 2 t 180 360 720 1 440 2 880 5 760d) 180 3 2 t > 40 000∴ 2 t > 222.22∴ t > 7.8∴ t 8 min2. a) 100% 2 5.5% 5 94.5%, which represents the volume of air that remains aftereach day.94.5b) V air5 4 200 3 (​ ____100 ​)t5 4 200 3 0.945 t , where t is the number of daysc) 2 671.18 cm 314 EXPLORING MATHEMATICS FORM 3