Question

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

Answer 1

Town ii is growing the fastest with a base of 1.12, while town v is decreasing the fastest with a base of 0.78.

Step-by-step explanation:

To determine which town is growing the fastest:

• we need to compare the growth rates of the population equations. The growth rate of an exponential equation is given by the base of the equation. In this case, the base is the number multiplied by the variable t, which represents time. The higher the base, the faster the population is growing. Comparing the bases of the exponential equations given, we can see that town ii has the highest base of 1.12, so it is growing the fastest. Therefore, the answer is (a) ii.

To determine which town is decreasing the fastest:

• we need to look at the negative growth rate, which is determined by the base of the equation when the number multiplied by t is less than 1. Comparing the bases of the exponential equations given, we can see that town v has the lowest base of 0.78, so it is decreasing the fastest. Therefore, the answer is (b) v.

Answer 2

For the first question it is: a. ii

For the second question it is b. V

Step-by-step explanation: