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Sagot :
Solution :
Transforming given equations :
[tex]1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t[/tex]
From above equations we can see that equation 1) has largest percentage growth rate and the percent growth rate is 12% .
Hence, this is the required solution.
Answer: (i), 12%
Step-by-step explanation:
Given
The Population of four towns is given
(i) [tex]P=600(1.12)^t[/tex] i.e.
[tex]\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t[/tex]
rate=12%
(ii) [tex]P=1000(1.03)^t[/tex]
[tex]\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t[/tex]
rate=3%
(iii) [tex]P=200(1.08)^t[/tex]
[tex]\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t[/tex]
rate=8%
(iv) [tex]P=900(0.90)^t[/tex]
[tex]\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t[/tex]
rate=10% fall
So, the largest growth rate is for town (i) i.e. 12%
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