A city that had 7500 thousand people at the beginning of the year 2000 has been decreasing by 3.6% per year. a. What is the 1-year percent change in the city's population. b. Whenever 1 year passes, the population becomes what percent of its previous value? (That is, the "new" population is what percent of the "old" population whenever 1 year passes?) c. What is the 1-year growth factor for the population of the city? d. Write a function g that determines the population of the city (in thousands of people) in terms of the number of years t since the beginning of 2000.

Question

Mathematics

Helena

21 April, 04:54

A city that had 7500 thousand people at the beginning of the year 2000 has been decreasing by 3.6% per year. a. What is the 1-year percent change in the city's population. b. Whenever 1 year passes, the population becomes what percent of its previous value? (That is, the "new" population is what percent of the "old" population whenever 1 year passes?) c. What is the 1-year growth factor for the population of the city? d. Write a function g that determines the population of the city (in thousands of people) in terms of the number of years t since the beginning of 2000.

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Answers (1)

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Nathalia Mathews · Answer 1

Step-by-step explanation:

a) if the population at the beginning of the year 2000 was 7500 people,

The 1-year percent change in the city's population would be

3.6/100 * 7500 = 270

b) The population after 1 year is

7500 - 270 = 7230

The percentage of the previous value of the population to its new value for each year is

7230/7500 * 100 = 96.4%

c) the 1-year growth factor for the population of the city would be

(1 - 0.036) ^1 = 0.964

d) the function, g that determines the population of the city (in thousands of people) in terms of the number of years t since the beginning of 2000 would be

g = 7500 (1 - 0.036) ^t

g = 7500 (0.964) ^t