Mathematics

Question

The deer population in a region is expected to decline 1.1% from 2010-2020. Assuming this continued how many deer would there be in the region in the year 2060 if the 2010 population was 1,578?


1,406

1,510

1,493

1,385

2 Answer

  • Answer:

    Option C. 1,493

    Step-by-step explanation:

    If the deer population in a region is expected to decline 1.1% from 2010 to 2020. Assuming this continued, we can say that the deer population decreases 1.1% each ten years.

    From 2010 to 2060 there are 50 years. If the deer population decreases 1.1% each ten years, then it will decrease 5.5% in 50 years.

    If the population in 2010 was 1,578. Then, the population in 2060 is going to be:

    Using the rule of three:

    If 1578 ----------------> Represents 100%

        X       <-----------------       5.5%

    X = (5.5%x1578)/100% = 86.79 ≈ 87

    Then the total population in 2060 is: 1578 - 87 = 1491

    None of the answers equal to 1491. That's why I assume the correct answer must be Option C. 1,493. Given that it's the closest answer!

  • Answer:

    The population would be 1,493.

    Step-by-step explanation:

    Given,

    The initial population, P = 1,578, (  In 2010 )

    Also, the decline rate per 10 years, r = 1.1 %,

    And, the number of the periods of 10 years since, 2010 to 2060, n = 5,

    Hence, the population in 2060 would be,

    [tex]A=P(1-\frac{r}{100})^n[/tex]

    [tex]=1578(1-\frac{1.1}{100})^5[/tex]

    [tex]=1493.09849208\approx 1493[/tex]

    Option third is correct.

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