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Logarithmic Functions as Inverses - Growth of Quail Population

by Brittany Knight
(South Carolina )










































Quail Population

An initial population of 745 quail increases at an annual rate of 16%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?

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Nov 21, 2012
Quail Population
by: Staff


Answer


Part I

Logarithmic Function and its Inverse

          The Inverse of a logarithmic function
          is an exponential function.

          The inverse of an exponential
          function is a logarithmic function.
          

     For example:

          Exponential Form

                    ay = x

          Logarithmic Form of the same
          function
           (the logarithm is “y”, the exponent)

                    y = logₐx

To calculate the value of a growth function, we will use the exponential form.

          The general form of an exponential growth function is:

                    V = abt

          V = value of function

          a = initial quantity

          b = growth factor

          t = time

          In addition, b, the growth factor = 1+g

          g = growth in 1 time period

          The final equation can be written as:

                    V = a(1 + g)t


----------------------------------------------------

Nov 21, 2012
Quail Population
by: Staff


----------------------------------------------------
Part II


When this is applied to your quail problem:

          V = calculated number of quail

          a = initial number of quail = 745 quail

          g = 16% increase per year (converted to decimal, g = 0.16)

          t = time in years = 4 years

          The equation for the growth of the quail population is:

                    V = a(1 + g)t

                    V = 745(1 + .16)4

                    V = 745(1.16)4

                    V ≈ 745(1.81063936)

                    V ≈ 1348.9263232000001



Final Answer:

V (Quail population after 4 years) ≈ 1349



Thanks for writing.

Staff
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