Percentage survivorship is a function of time; there ia negligible decline in survivorship at pH=6, marked decline in survivorship at pH=3.5, resulting in no survivors after just 8 hours.

What is the function for this problem and how do I plot it in Maple?

The rate of resource consumption by organisms,v depends on resource concentration, S. The Blackman model of resource consumption assumes a linear relationship between v and S. Below a threshold concentration, S_k , consumption rate increases linearly with S=0 when v=0; when S=S_k, v reaches its max value, v_max. For S> S_k, v stays at v_max.

The function like this is defined piecewise,

  v= { g(S)   for 0<=S< S_k

         vmax  for S>=Sk

g(S)=( v_max/S_k).S

How do I graph v as a function of S with the graph showing the point where S_k=v_max?

Egg development

It takes 3 days at 20^oC, but almost 20 days at 5^oC for an egg to develop and hatch. When graphed on log -log plot, it says that egg development time (in days) as a function of temperature (in ^oC) is a straight line.

How do I sketch the log-log graph in Maple?

The chemical reaction is given as

A+2B ---> AB₂

The reaction occurs ina closed vessel and the initial concentration of A=[a] and B=[b]

The reaction rate is given by

R(x)= k(a-x)(b-2x)²

where x=[AB₂]

Graph R(x) for the relevant values of x when a=5,b=6 and k=0.3.

Let

f(x)= 2x^2 -2, x >= 0

Find d/dx f^-1(x)|(subscript x=0.)

Note that f(1)=0.

Use d/dx f^-1(x)= 1/(f'[f^-1(x)])