Under evolving carbon tax legislation, companies must strategically determine the optimal timing for their investments, carefully balancing the performance of available technologies in terms of emission reductions and investment costs to maximize benefits. To address this problem, we develop and solve a multi-period mixed integer (MPMI) model for technology selection under a progressive linear carbon tax legislation. The model is then analyzed analytically by implementing various algorithms to calculate and compare a range of profitable investment decisions until the optimal one is identified. In the light of the performance of the available technologies (costs and emissions) and the applied dynamic carbon tax scheme, we characterize the optimal year of investing in green and determine the duration for sustaining a profitable business. Through analytical and numerical analyses, we underline how governments should take into consideration this aspect to enact efficient taxes for different industrial sectors to push them toward greening their supply chains without eroding their profits. For instance, we show that high-emission industries are likely to invest in green technology from the first year if it offers significant carbon reduction capabilities. Otherwise implementing progressive carbon taxation policies could harm profitability and force these industries out of business.