A population of ants is growing at a rate of 8% a year. If there are 160 ants in the initial population, find the number of ants after 6 years

253 ants

Step-by-step explanation:

160 ants to begin with.

8% yearly growth

8% of 160 is 12.8

for year 2, 8% of 172.8 is 13.824

then 8% of 186.624 is 14.92992

year 4: 8% of 201.55392 is 16.1243136

5: 8% of 217.6782336 is 17.4142586

finally, year 6: 8% of 235.092492288 is 18.807399383

so the total ants after 6 years is 253.899891671

but you cant have. 8 ant so drop the decimal

The number of ants after 6 years will be 253.

Step-by-step explanation:

8% + 100% = 108% = 108 / 100 = 1.08

The n-th term of a geometric sequence with initial value a1 and common ratio r is given by:

an = a1 ∙ r ⁿ⁻¹

In this case:

a1 = 160

r = 1.08

Need to notice that term two is after one year, so term 7 will be after 6 years.

n = 7

so:

a6 = a1 ∙ r⁷⁻¹

a6 = 160 ∙ r⁶

a6 = 160 ∙ 1.08⁶

a6 = 160 ∙ 1.586874322944

a6 = 253.89989167104