Question

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

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.