A species of animal is discovered on an island. Suppose that the population size of the species can be modeled by the following function, wh

Question

A species of animal is discovered on an island. Suppose that the population size of the species can be modeled by the following function, where time t is measured in years. P(t) = 520/1 + 8e-0.3t Find the initial population size of the species and the population size after years.

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Euphemia 5 months 2021-08-13T17:34:53+00:00 1 Answers 56 views 0

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    2021-08-13T17:35:55+00:00

    Answer:

    The initial population size is of 58.

    The population size of the specie after t years is given by:

    *** QuickLaTeX cannot compile formula:
    P(t) = \frac{520}{1 + 8e^{-0.3t}
    
    *** Error message:
    File ended while scanning use of \frac .
    Emergency stop.
    
    

    Step-by-step explanation:

    Population size of the specie:

    The population size of the specie after t years is given by:

    *** QuickLaTeX cannot compile formula:
    P(t) = \frac{520}{1 + 8e^{-0.3t}
    
    *** Error message:
    File ended while scanning use of \frac .
    Emergency stop.
    
    

    Initial population size

    This is P when t = 0, that is, P(0). So

    *** QuickLaTeX cannot compile formula:
    P(0) = \frac{520}{1 + 8e^{-0.3*0} = \frac{520}{1+8} = \frac{520}{9} = 57.7
    
    *** Error message:
    File ended while scanning use of \frac .
    Emergency stop.
    
    

    Rounding to the nearest number, 58

    The initial population size is of 58.

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