Hi there!
[tex]\large\boxed{\text{p(x) = 4(3)^{x}, q(x) = 4(2)^{x}}}[/tex][tex]\large\boxed{p(x) = 4(3)^{x}}}\\\large\boxed{ q(x) = 4(2)^{x}}[/tex]
(a)
Looking at the graphs, we see that both p(x) and q(x) intersect the y-axis at
y = 4, or (0, 4).
(b)
The base of the functions is simply the value of the y-intercept, or a = 4.
(c)
We can write equations for both using an external point at x = 1:
p(x):
y = 4(b)^x
Plug in the point (1, 12) to solve:
12 = 4(b)^1
12 = 4b
b = 3
Rewrite the equation:
[tex]p(x) = 4(3)^{x}[/tex]
q(x):
y = 4(b)^x, plug in the point (1, 8):
8 = 4(b)^1
8 = 4b
b = 2
Rewrite:
[tex]q(x) = 4(2)^{x}[/tex]
