Question

The populations, P, of six towns with time t in years are given by

Answer 1

Answer:

Since, in the population function,

$P = ab^t$

a = initial population,

b = population change factor,

If 0 < b < 1, then population will shrink,

While, if b > 1, then the population will grow,

(a) Since, 1.18, 1.08 and 1.191 is greater than 1,

Thus, town 4), 5) and 6) are growing.

(b) Since, 0.8, 0.77 and 0.98 are less than 1,

Thus, town 1), 2) and 3) are shrinking.

(c) An exponential growth function with highest change factor grows fastest.

∵ 1.191 > 1.18 > 1.08

⇒ town 6) is growing fastest.

(d) An exponential decay function with lowest change factor shrinks fastest,

∵ 0.77 < 0.8 < 0.98 < 1.08 < 1.18 < 1.191,

⇒ Town 2) shrinks fastest.

(e) Since,

2400 > 2100 > 1700 > 1100 > 900 > 600

⇒ town 1) has the largest initial population.

(f) Similarly,

Town 4) has the smallest initial population.