Sort of. Need to be careful of terminology: t_{k} is an experimentally determined data point. Equation 1 is the idealized function that is suppose to represent the data, but doesn't precisely do so because of experimental error associated with the data points. The method to estimate the parameters a & b is least squares. Equation 2 is the least squares problem to solve based on the desired fitting function (i.e. equation 1).
Thus, if you have a bunch of experimentally determined data points t_{k}, estimates of the parameters a & b can be found by minimizing equation 2. I hope this helps explain the situation.
One thing that seems odd is the use of k in equation 2. The index k is meant to represent the index of data points, but k is also used within the fitting function itself (i.e. equation 1). Either that's a typo or the "x" values associated with the data points is really 0,1,2...n.
