Question

The population of a city has been increasing at a rate of 1.2% per year. The population was 125,000 in the year 2000.

a) find the population in 2012.

b) estimate the year when the population will be 200,000

Answer 1

every year the difference between population is 1.2%(i.e 1.2/100)
a = 125,000
d = 1.2/100

a). \[a_n = a_0 +(n-1)d\]
n = 2012 - 2000 = 12years
\[a_n = 125,000 +(12-1)*(1.2/100)\]

b) \[a_n = a_0 +(n-1)d\]
an = 200,000
a0 = 125,000
d = 1.2/100
find n

Answer 2

can you help me find n??

Answer 3

@sangya21

Answer 4

okkk wait
total population = 200,000
sum = (n/2) [2a + (n-1)d]
200,000 = (n/2)[2* 125,000 +(n-1) 1.2/100]
200,00 = 125,000n + (1.2/100)n *(n/2) -(1.2/100)*n/2
200,000 = 0.6n^2/100 +(125,000n - 0.6n/100)