Page 13 - Modul A+1 Matematik Tingkatan 5

Uji Kendiri 8.1
1. Sesetengah populasi bakteria akan membiak tiga kali ganda setiap jam selepas suatu eksperimen bermula. Uji kaji akan
berakhir sebelum 20 000 populasi bakteria dihasilkan.
Some bacteria population will breed triple every hours after an experiment begins. The experiment will end before 20 000 bacteria’s
population been produced.
Bentukkan satu model matematik untuk menentukan masa eksperimen ini akan dihentikan.
Form a mathematical model to determine the time when the experiment will be stopped. KBAT Menganalisis
Panduan murid/Student’s guide:
(1) Menentukan masa eksperimen akan dihentikan/Determine the time when the experiment stopped.
(2) Andaian: Semakin meningkat tempoh masa, populasi bakteria semakin bertambah.
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Assumption: The higher the duration of time, the population of bacteria is increase.
Pemboleh ubah/Variable:
(a) Tempoh masa (jam)/Duration of time (hour)
(b) Populasi bakteria/The population of bacteria
(3) Jadual data/Data table
Tempoh masa (jam)/Duration of time (hour) 1 1 2 … n

Populasi bakteria/Population of bacteria 1 3 9
Rumus/Formula 3 0 3 1 3 2 … 3 n

(4) Memplot graf populasi bakteria melawan tempoh masa.
Plotting a graph of population of bacteria against duration of time.

Populasi bakteria
Population of bacteria

9
8

7

6 BAB 8

5

4

3

2
1

Tempoh masa
–3 –2 –1 0 1 2 3 Duration of time

n
(5) y = 3 , dengan keadaan populasi bakteria ialah y dan tempoh masa ialah n
where the population of bateria is y and duration of time is n
Cari penyelesaian berdasarkan graf:
Find the solution based on graph:
3  20 000
n log 3  log 20 000

n  log 20 000
log 3
n  9
(6) Maka, pada jam ke-9, eksperimen akan dihentikan kerana 19 683 bakteria telah dihasilkan, iaitu paling hampir
dengan kadar uji kaji terakhir.
Thus, in the 9th hours, the experiment will be stopped because 19 683 bacterias have been produced, which is closest to the last
experimental rate.

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08 ModulA+ Matematik Tg5.indd 155 08/10/2021 2:45 PM