Consider the exponential equation y = 47(0.9)x. Several points satisfying the equation are shown in the calculator table. Notice that when x = 0, y = 47.
a. The expression 47(0.9)x could be rewritten as 47(0.9)(0.9)x - 1. Explain why this is true. Rewrite 47(0.9)(0.9)x - 1 in the form a · bx - 1.
b. The expression 47(0.9)x could also be rewritten as 47(0.9)(0.9)(0.9)x - 2. Rewrite 47(0.9)(0.9)(0.9)x - 2 in the form a · bx - 2.
c. Look for a connection between your answers to 11a and b, and the values in the table. State a conjecture or general equation that generalizes your findings?