We can model this situation with an initial population a=400,000.
The rate of change of the population is -6%, so the population at year x=1 will be:
[tex]y(1)=400,000\cdot(1-0.06)=400,000\cdot0.94=376,000[/tex]The second year (x=2), the population will decrease another 6%:
[tex]y(2)=376,000\cdot0.94=353,440=400,000\cdot(1-0.06)^2[/tex]We can generalize this as:
[tex]y(x)=400,000\cdot(1-0.06)^x[/tex]Then, ten years from now (x=10), the population will be:
[tex]y(10)=400,000\cdot(1-0.06)^{10}\approx400,000\cdot0.5386\approx215,446[/tex]The expected population 10 years from now is 215,446 elephants.
