In studying salmon populations, a model often used is the Ricker equation which relates the size of a fish population this year,
x to the expected size next year y. (Note that these populations do not change continuously, since all the parents die before the eggs are hatched.) The Ricker equation is
y = axe^(-bx) where a,b> 0
Find the value of the current population which maximizes the salmon population next year according to this model.
---> I differentiated it this far:
dy/dx = axe(-bx)(-b) + e^(-bx)(a)
dy/dx = -axe^(-bx)b + ae^(-bx)
dy/dx = 0 = ae^(-bx) (-xb + 1)
in the question we are given that a,b>0 Could anyone please tell me how to further solve this question??