1. This is an exponential function with general form [tex]y=a(b^x)[/tex]. It passes through (0, 3), (1, 6), and (2, 12). It starts at y = 3, so a = 3. For every 1 unit increase in x, the y-value doubles, so b = 2. Therefore, the equation for this graph is [tex]y = 3(2^x)[/tex].
2. Since b = 0.42 (which is < 1), this is decaying. The multiplier is -3. The function is decreasing by 58% (1 - 0.42 = 0.58). This is shifted 16 units to the left (the exponent is x + 16), and 9 units down.
3. [tex]f(n) = -0.9(2^{3n})+0.2 \\ f(2) = -0.9(2^{6})+0.2 \\ f(2) = -57.4[/tex]
