Question

Country A has a population of ?(?) = 75(0.83) ? where t is the number of years after 2000 and ?(?) is the population of country A in millions of people. Country B has a population of ?(?) = 20(1.2) ? where t is the number of years after 2000 and ?(?) is the population of country B in millions of people. (a) Graph both functions on the same axis for the years 2000 through 2010. (b) What was the population of each country in 2000? (c) Write complete sentences to describe exactly how the population of each country is changing. (d) Graphically find A(2) and B(2). Then write a sentence that interprets the real world meaning of what you have found. (e) Graphically solve A(t)=60 and B(t)=60. Then write a sentence that interprets the real world meaning of what you have found. (f) Graphically solve A(t)=B(t). Then write a sentence that interprets the real world meaning of what you have found.

Answer 1

(a)

t	A(t) = 75(0.83^t)	B(t) = 20(1.2^t)
0	75	20
1	62.25	24
2	51.6675	28.8
3	42.884025	34.56
4	35.59374075	41.472
5	29.54280482	49.7664
6	24.520528	59.71968
7	20.35203824	71.663616
8	16.89219174	85.9963392
9	14.02051915	103.195607
10	11.63703089	123.8347284

(b) A(0) = 75 millions and B(0) = 20 millions

(c) Population of country A is decreasing exponentially and population of country B is increasing exponentially

(d) A(2) = 52 million (approximately) and B(2) = 29 million approximately). These are the populations of A and B respectively in the year 2002

(e) A(t) = 60 for t = 1.2 years (approximately) and B(t) = 60 for t = 6 years (approximately)

Population of A will be 60 million between the years 2001 and 2002. Population of B will be 60 million in the year 2006

(f) A(t) = B(t) for t = 3.6 years (approximately). This means populations of A and B will be equal between the years 2003 and 2004.

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