The tiger population loses 3/5 of its size every 2.94 decades
Rate of change using differential calculus
The given equation is:
[tex]N(t)=710(\frac{8}{125} )^t[/tex]
Find the derivative of the given function
[tex]\frac{dN}{dt} =710(0.064)^tln(0.064)\\\\\frac{dN}{dt} =-1951.7(0.064)^t[/tex]
When the tiger loses 3/5 of its population
dN/dt = 3/5
Solve for t
[tex]\frac{3}{5} =-1951.7(0.064)^t\\\\-0.0003=(0.064)^t[/tex]
Take the natural logarithm of both sides
[tex]ln(-0.0003)=t(ln0.064)\\\\-8.087=-2.75t\\\\t=\frac{-8.087}{-2.75} \\\\t=2.94[/tex]
The tiger population loses 3/5 of its size every 2.94 decades
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