Yes, it is true the cells of organisms use energy for growth and repair.
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Exponential growth implies that the rate of growth increases as time passes. So, it's not that "one cell" becomes "two cells" in two seconds and "three cells" in three seconds - that's linear growth. If you plot a chart of "Number of cells" against "Time" or "Number of cycles", the number of cells increases with a ratio greater than 1:1 each time unit or cycle.
Cells have multiple sources of nutrients including fats and sugars, that can be used to create energy. As far as sugar is concerned, glucose is the sugar that is used by cells to produce energy.
provide energy to the cells
The Seven Properties of Life:-made up of cells-reproduction-based on genetic code-growth and development-need for materials and energy-response to environment- maintaining internal balance
Because the genes that are expressed affect every aspect of the cell, from the look and size of the cell to what chemical actions it can carry out, being able to turn some genes off and others on allows the cells to both respond to their environment and, in the case of multicellular organisms, have different types of cells. If the cells in the human body could not regulate their gene expressions then the cells of the liver would be the exact same as the cells of the heart and they would be the same as every other cell. In this situation complex organisms could not exist as we know them.