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11 June, 18:01

The population of an endangered species of insect is 480,000. The population decreases at the rate of 10% per year. Identify the exponential decay function to model the situation. Then find the population of the species after 3 years.

A: y = 480,000 (1.01) t; 280,000

B: y = 480,000 (1.1) t; 638,880

C: y = 480,000 (0.9) t; 339,940

D: y = 480,000 (0.9) t; 349,920 5

Cesium-137 has a half-life of 30 years. Identify the amount of cesium-137 left from a 150 milligram sample after 120 years.

A: 0.9375 mg

B: 9.3750 mg

C: 1.097 mg

D: 1.325 mg 6

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  1. 11 June, 20:55
    0
    D: y = 480,000 (0.9) t; 349,920

    Step-by-step explanation:

    The question requires us to model a compounding exponential decay function at a given rate for a particular period:

    Using the model:

    F = Fo (1 - r) ^t

    Where;

    F = final amount; Fo = Initial amount; r = annual rate; t = period

    Initial amount = 480,000

    Rate = 10%

    t = 3years

    F = 480,000 (1 - 0.1) ^3

    F = 480,000 (0.9) ^3

    F = 480,000 * 0.729

    F = 349, 920

    A = (Ao / 2^ (t/t1/2)

    A = final amount

    Ao = Initial amount

    t = time or period; t1/2 = half-life = 30 years

    A = (150 / 2^ (120/30))

    A = (150 / 2^ (4))

    A = 150/16

    A = 9.375mg
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