Eniki has a sequence of numbers given by the formula t(n) = 4(5ⁿ).

1. What are the first three terms of Eniki's sequence?

   Hint (a):

   Substitute n = 1, 2, and 3 into the formula.

2. Chelita thinks the number 312,500 is a term in Eniki's sequence. Is she correct? Justify your answer by either giving the term number or explaining why it is not in the sequence.

   Hint (b):

   Let t(n) = 312,500 and solve for n. Be sure to divide both sides of the equation by 4 before taking the log of both sides.

   More Help (b):

   What kinds of numbers will tell you if it is in the sequence?

3. Elisa thinks the number 94,500 is a term in Eniki's sequence. Is she correct? Explain.

   Hint (c):

   See part (b).