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 th…

Question

asked Sep 20, 2022 44.8k views

2 Answers

MrRoman · Answer 1 · 2022-09-21T09:59:59+0000

Solution :

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.

Koichi · Answer 2 · 2022-09-26T02:31:34+0000

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%