Consider an idealized population with the characteristic that each member of the population produces one offspring at the end of every time period. Each member has a life span of three time periods and the population begins with 10 newborn members. The following table shows the population during the first five time periods.

The sequence for the total population has the property that

Find the total population during each of the next five time periods.

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Age Bracket 0-1 1-2 2-3 Total Time Period 1 2 3 4 5 10 10 20 40 70 10 10 20 40 10 10 20 10 20 40 70 13 130