Question

The population, P, of six towns with time t in years are given by the following exponential equations:

(i) P = 1000 (1.08) Superscript t (ii) P = 600 (1.12) Superscript t
(iii) P = 2500 (0.9) Superscript t (iv) P = 1200 (1.185) Superscript t
(v) P = 800 (0.78) Superscript t (vi) 2000 (0.99) Superscript t
Which town decreasing the fastest?
a.
ii
c.
iii
b.
v
d.
vi



Please select the best answer from the choices provided


A
B
C
D

Answer 1

Given:

The population, P, of six towns with time t in years are given by the following exponential equations:

(i)
`P=1000(1.08)^t`

(ii)
`P = 600 (1.12)^2`

(iii)
`P =2500 (0.9)^t`

(iv)
`P=1200 (1.185)^t`

(v)
`P=800 (0.78)^t`

(vi)
`P=2000 (0.99)^t`

To find:

The town whose population is decreasing the fastest.

Solution:

The general form of an exponential function is:

`P(t)=ab^t`

Where, a is the initial value, b is the growth or decay factor.

If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.

The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town
`P=800 (0.78)^t` is decreasing the fastest.

Therefore, the correct option is b.