Question

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.

Answer 1

Answer:

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

Answer 2

The 1-year percent change in the city's population is = 270.

The percentage of the previous value of the population to its new value for each year is, 96%.

The 1-year growth factor for the population of the city would be 0.96.

The number of years t since the beginning of 2000 is,

$g = 7500 (1-0.036)^{t} \\\\g = 7500 (0.964)^{t}$

Given that,

At the beginning of the year 2000 city population is = 7500 thousand

The 1-year percent change in the city's population would be = 3.6% per year.

According to the question,

• The 1-year percent change in the city's population is ,

= $\frac{3.6}{100}$ × 7500 = 270

• 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,

$\frac{7230}{7500}$ × 100 = 96.4%

• The 1-year growth factor for the population of the city would be,

$( 1- 0.036 )^{1}$ = 0.964

• 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,

$g = 7500 (1-0.036)^{t} \\\\g = 7500 (0.964)^{t}$

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