Question

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

(i) P=600(1.12)^t
(ii) P=1,000(1.03)^t
(iii) P=200(1.08)^t
(iv) P=900(0.90)^t
Which town has the largest percent growth rate? What is the percent growth rate?

Answer 1

Transforming given equations :

`1)\ P = 600( 1 + (12)/(100))^t\\\\2)\ P = 1000( 1 + (3)/(100))^t\\\\3)\ P = 200( 1 + (8)/(100))^t\\\\4)\ P = 900( 1 - (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%

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%