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?

Comments for Logarithmic Functions as Inverses - Growth of Quail Population

 Nov 21, 2012 Quail Population by: Staff AnswerPart ILogarithmic 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 = logₐxTo 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 www.solving-math-problems.com

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