The population, P, of six towns with time t in years are given by the following exponential equations: (i) P = 1000(1.08)t
(iii) P = 2500(0.9)t
(v) P = 800(0.78)t
(ii) P = 600(1.12)t
(iv) P= 1200(1.185)t
(vi) 2000(0.99)t

which town is growing fastest?

a. ii

b. v

c. iii

d. vi

and

which town is decreasing the fastest?

a. ii

b. v

c. iii

d. vi

1. Town IV

2. Town V

Step-by-step explanation:

To find the town decreasing or growing fastest, let’s have the same value of years

Mathematically, we can write the values as follows;

P = I(1 + r)^t

where r is the growth percentage;

i. 1000(1 + 0.08)^t

ii 2500(1-0.1)^t

iii 800(1-0.22)^t

iv 600(1 + 0.12)^t

v 1200(1 + 0.185)^t

vi 2000(1-0.01)^t

Now the term that grows fastest have the highest value of r. That is the highest positive value attached to 1 while the one that grows slowest has the highest negative value subtracted from 1

For the first set of questions, out of all the options, answer is town V

It is the only positive r, all others are decreasing

For the second question, answer is town iii, it has the biggest negative value for r

the answer to the expression is 83