The provided formulas for calculating copy number in qPCR are used for different purposes: the first for absolute quantification based on a standard curve and the second for relative quantification normalized to a reference gene. It's important to consider reaction efficiency and choose the appropriate method for your experimental setup.
The question you have asked pertains to the calculation of copy number in quantitative PCR (qPCR) experiments. The two formulas you've found both serve different purposes. The formula copy number = 10^((CT - intercept)/(-slope)) is used in absolute quantification to calculate the number of copies of DNA based on a standard curve. This requires that you have a standard curve with known concentrations of DNA to generate the slope and intercept values used in the formula. The efficiency of the PCR reaction can be derived from the slope of the standard curve, with an ideal slope being around -3.32 which corresponds to nearly 100% efficiency.
The common alternative formula, copy number = 2^-ΔΔCt, is used in relative quantification to compare the expression of a target gene in different samples, normalized to a reference gene. ΔΔCt is the difference in threshold cycles for target and reference genes, adjusted for control or calibrator samples.
For further refinement of your calculations, it is critical to include considerations of reaction efficiency and to use the most appropriate method of analysis for your experimental design.