Question

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Answer 1

The tiger population loses 3/5 of its size every 2.94 decades

Rate of change using differential calculus

The given equation is:

$N(t)=710(\frac{8}{125} )^t$

Find the derivative of the given function

$\frac{dN}{dt} =710(0.064)^tln(0.064)\\\\\frac{dN}{dt} =-1951.7(0.064)^t$

When the tiger loses 3/5 of its population

dN/dt = 3/5

Solve for t

$\frac{3}{5} =-1951.7(0.064)^t\\\\-0.0003=(0.064)^t$

Take the natural logarithm of both sides

$ln(-0.0003)=t(ln0.064)\\\\-8.087=-2.75t\\\\t=\frac{-8.087}{-2.75} \\\\t=2.94$

The tiger population loses 3/5 of its size every 2.94 decades

Learn more on rate of change using calculus here: brainly.com/question/96116

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