They collect energy from the sun and use carbon dioxide and water in the process called photosynthesis to produce sugars. Animals can make use of the sugars provided by the plants in their own cellular energy factories, the mitochondria.
Growth cycles are recurrent fluctuations in the series of deviations from trend. Thus, growth cycle contractions include slowdowns as well as absolute declines in activity, whereas business cycles contractions includes only absolute declines (recessions).
These both are related because both of these cycles run on another source, to obtain any type of energy you need food, etc. Growth cycles occur when they obtain energy and or have something to give them energy to have a continuous cycle.