Question

During the 1960s the concentrations of PCBs in Great Lakes fish started to increase as this pollutant became more and more ubiquitous. The following are PCB concentrations in Lake Michigan bloaters as a function of time (year, concentration in ppm): 1958, 0.03; 1960, 2.32; 1962, 4.37; 1964, 5.51; 1966, 6.60; 1968, 7.03; and 1972, 7.26. What is the rate constant associated with the accumulation of PCBs in these fish?

Answer 1

his is the situation in which the concentration starts at zero and goes up to a steady-state value.

We have such equation for these conditions:

$C = C_{max}(1 – exp(-kt))$

Our task is to find k.

I will use a tool in Excel called “Solver.”

And after applying "Solver" tool for minimizing the sum of squared residuals.

Answer: 0.24 year^-1