Could someone me step by step with this question?

Which approach to the theory-and-research cycle does the following sequence reflect: (1) specific observations suggest generalizations, (2) generalizations produce a tentative theory, (3) the theory is tested through the formation of hypotheses, and (4) hypotheses may provide suggestions for additional observations?

Consider the input and output values for f(x) = 2x - 3 and g(x) = 2x + 7. what is a reasonable explanation for different rules with different input values producing the same sequence?

Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of cate's stock be about $2000