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.
