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27 December, 21:22

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

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  1. 27 December, 21:23
    0
    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
  2. 27 December, 21:50
    0
    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
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