Question 1118985
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Generation 0: N = 10; r = 0.6<br>
Generation 1: N(new) = r*N+N = 0.6(10)+10 = 6+10 = 16; r = 0.6<br>
Generation 2: N(new) = r*N+N = 0.6(16)+16 = 9.6+16 = 25.6<br>
Answer c<br>
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I hope this problem is from an introductory lesson on exponential growth.  The recursive process used is extremely inefficient; to find the population after 20 generations you would have to perform the defined calculation 20 times.<br>
It is far more efficient to use an explicit formula for the population after n generations.  The recursive formula for the new population size,<br>
{{{r*N+N}}}<br>
can be written as<br>
{{{N(r+1)}}}  or  {{{N(1+r)}}};<br>
then the population after n generations is simply the beginning population, multiplied by the "growth factor" (1+r) n times:<br>
{{{P(n) = N(1+r)^n}}}<br>
For your problem the populations after 1 and 2 generations are then<br>
{{{P(1) = 10(1.6) = 16}}}
{{{P(2) = 10(1.6)^2 = 10(2.56) = 25.6}}}<br>
To find the population after 10 generations by the recursive method would be very tedious; with this method it is a single calculation:<br>
{{{P(10) = 10(1.6)^10 = 1100}}} (to the nearest whole number)