The growth of a local raccoon population approximates a geometric sequence where an is the number of raccoons in a given year and n is the y

Question

The growth of a local raccoon population approximates a geometric sequence where an is the number of raccoons in a given year and n is the year. after 6 years there are 45 raccoons and after 8 years there are 71 raccoons.

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Amaya 3 months 2021-10-20T00:13:51+00:00 1 Answer 0 views 0

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    2021-10-20T00:15:00+00:00

    Answer:

     GENERAL EXPLICIT SEQUENCE IS GIVEN   a_n = (14.74)(r)^{n-1)}

    Step-by-step explanation:

    Let n be the number of year the data is recorded in.

    a: The number of raccoons taken initially.

    r: The multiplying factor

    a_n  : The number of raccoon in the nth year.

    As given:  a_6 = 45, a_8 = 71

    Now, as the given situation can be expressed as GEOMETRIC SERIES:

    a_n  = a r^{(n-1)}

    Applying the same to given terms, we get:

    a_6 =  a r^{(6-1)} = ar^5 = 45\\\implies ar^5 = 45

    a_8 =  a r^{(8-1)} = ar^7 =71\\\implies ar^7 = 71

    Dividing both equations, we get:

    \frac{ar^7}{ar^5}  = \frac{71}{45}  \\\implies r^2 = 1.58\\\implies r = 1.25

    So, the first term a = \frac{45}{(1.25)^5}  = 14 .74 \approx 15

    So, the GENERAL EXPLICIT SEQUENCE IS GIVEN as:  a_n = (14.74)(r)^{n-1)}

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45:7+7-4:2-5:5*4+35:2 =? ( )