Question

The following functions give the populations of four towns with time tt in years.

Answer 1

Solution :

Transforming given equations :

$1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t$

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 2

Answer: (i), 12%

Step-by-step explanation:

Given

The Population of four towns is given

(i) $P=600(1.12)^t$ i.e.

$\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t$

rate=12%

(ii) $P=1000(1.03)^t$

$\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t$

rate=3%

(iii) $P=200(1.08)^t$

$\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t$

rate=8%

(iv) $P=900(0.90)^t$

$\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t$

rate=10% fall

So, the largest growth rate is for town (i)  i.e. 12%