For 13–17, use the table at right. The table gives the populations of Toledo, Ohio, and Lexington, Kentucky, during the last three U. S. Censuses.

13)2000 per year

14)a_n = 350000 - 2000(n - 1)

15)3000 per year

16)a_n = 200000 + 3000(n - 1)

17)when when the number of years is more than 31 years, Lexington's population will be greater than toledo.

Step-by-step explanation:

13) From the table, the population of toledo is 350,000 in 1980 and 330000 in 1990.

Thus,population change from 1980 to 1990 is; 350000 - 330000 = 20000

Similarly, from 1990 to 2000, population went from 330000 to 310000. Change in population is; 330000 - 310000 = 20000

In both cases we see that in 10 years interval, the change is 20000 each.. Thus, for 1 year, change in population = 20000/10 = 2000 per year

14) The population of toledo after 1980 can be expressed using arithmetic progression. Formula is;

a_n = a + (n - 1)d

Where;

a is population in 1980

n is number of years after 1980

d is change in population per year.

Since the population decreases each year, then d will be negative. Thus;

Thus;. a_n = 350000 - 2000(n - 1)

15)From the table, the population of lexington is 200,000 in 1980 and 230000 in 1990.

Thus,population change from 1980 to 1990 is; 230000 - 200000 = 30000

Similarly, from 1990 to 2000, population went from 230000 to 260000. Change in population is; 260000 - 230000 = 30000

In both cases we see that in 10 years interval, the change is 30000 each.. Thus, for 1 year, change in population = 30000/10 = 3000 per year

16) like earlier stated The population of Lexington after 1980 can be expressed using arithmetic progression. Formula is;

a_n = a + (n - 1)d

Where;

a is population in 1980

n is number of years after 1980

d is change in population per year.

a_n = 200000 + 3000(n - 1)

17) we want to find the years in which the population of Lexington will be more than that of toledo.

This simply means the inequality is;

200000 + 3000(n - 1) > 350000 - 2000(n - 1)

Deduct 200000 from both sides;

200000 - 200000 + 3000(n - 1) > 350000 - 200000 - 2000(n - 1)

3000(n - 1) > 150000 - 2000(n - 1)

Add 2000(n - 1) to both sides to get;

3000(n - 1) + 2000(n - 1) > 150000

3000n - 3000 + 2000n - 2000 > 150000

5000n - 5000 > 150000

5000n > 150000 + 5000

5000n > 155000

n > 155000/5000

n > 31

Thus,when when the number of years is more than 31 years, Lexington's population will be greater than toledo.