Question

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

1) P=2400(0.8)^t

2) P=900(0.77)^t

3)P=2100(0.98)^t

4)P=600(1.18)^t

5)P=1100(1.08)^t

6)P=1700(1.191)^t

Answer the following questions regarding the populations of the six towns above. Whenever you need to enter several towns in one answer, enter your answer as a comma separated list of numbers. For example if town 1, town 2, town 3, and town 4, are all growing you could enter 1, 2, 3, 4 ; or 2, 4, 1, 3 ; or any other order of these four numerals separated by commas.

(a) Which of the towns are growing?

(b) Which of the towns are shrinking?

(c) Which town is growing the fastest?
What is the annual percentage growth RATE of that town? %

(d) Which town is shrinking the fastest?
What is the annual percentage decay RATE of that town? %

(e) Which town has the largest initial population?

(f) Which town has the smallest initial population?

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.

Answer 2

Answer:

a.

i, ii, and iv

Step-by-step explanation: