Answer the following questions regarding the populations of the six towns above.

Question

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?  

1 2 3 4 5 6 The population, P, of six towns with time t in years are given by Answer the following questions regarding the population 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 enter1, 2, 3, 4; or 2, 4, 1, 3; or any other order of these four numerals separated by commas. Which of the town are growing? Which of the town are shrinking? Which town is growing the fastest? What is the annual percentage growth RATE of that town? Which town is shrinking the fastest? What is the annual percentage decay RATE of that town? Which town has the largest initial population? Which town has the smallest initial population?

Explanation / Answer

Recall that if in the function y=a*(b)x , if b>1 then function is increasing and if b<1 then function is decreasing.

Hence from the given Data we can observe that:

(a) Which of the towns are growing:

The base of the exponent terms is greate than 1 in the towns 1,3,4.

hence the towns that are growing are: 1,3,4

(b) Which of the towns are shrinking:

The base is less than 1 in the towns, 2,5 and 6.

hence the towns that are shrinking are: 2,5,6

(c) Which town is growing the fastest:

Since the base of the exponent term is gretest in town 1, hence the fastest growing town is: 1

And the annual percent growth rate is 0.193 or 19.3%

(d) Which town is shrinking the fastest:

The lowest base of exponent term is in town 2, hence the fastest shrinking town is : 2

and the decay rate is 1-0.74 or 0.26. So decay rate is 26%.

(e) Which town has the largest initial population:

The initial value of the function in y=a*(b)x is given by 'a'.

so from the given data we can see that the town 5 has the maximum population of 2000 initially.

Hence the town that has largest initial population is: 5

(f) Which town has the smallest initial population:

And the town with smallest initial population of 500 is town 3.

Hence the town that has smallest initial population is: 3

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