If 100 animals are released in a game preserve, the populationgrows according to

Question

If 100 animals are released in a game preserve, the populationgrows according to the model       p = 1000            1+9e -4t         wherep is the population at time t (where t is in years). Find the population after 5 years. Thank you!              If 100 animals are released in a game preserve, the populationgrows according to the model       p = 1000            1+9e -4t         wherep is the population at time t (where t is in years). Find the population after 5 years. Thank you! Find the population after 5 years. Thank you!             

Explanation / Answer

You are asked to find p, given the equation p = 1000 / (1 + 9e-4t) and given t = 5. This is a VERY unusual population equation. Are you sure thenumerator of the equation isn't supposed to be 100, the startingpopulation? (at t = 0, the population is immediately 1,000,which isn't correct if you are starting with 100) The "normal" population exponential growth equation is p =xet/to where p is the population aftera given time t, x is the starting population, e is a constant, andto is the starting year/date . With e to anegative exponent, this means the population will DECREASE (i.e.like radioactive decay with a half-life). Assuming 1000 is correct, Therefore, p = 1000/ (1 + 9e-20) e = 2.71828183 Therefore 1+ 9e-20 = 1.00000001855 p = 1000/(1+ 9e-20) = 999.999 However, as I said, this doesn't appear to be the correctformula.

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