Remember that a exponential function is of the form
y=a(b^x)
where
a is the initial value or y-intercept
b is the base of the exponential function
In this problem we have
For x=1 ------> y=3
so
substitute
3=a(b^1)
3=ab
a=3/b -------> equation 1
For x=2, y=9
so
9=a(b^2)
ab^2=9
a=9/b^2 ------> equation 2
equate equation 1 and equation 2
3/b=9/b^2
solve for b
9/3=b^2/b
3=b
Find the value of a
a=3/b
a=3/3
a=1
therefore
the equation is
y=3^x
Find the rate of change
we have that
b=1+r
where
r is the rate of change
substitute
3=1+r
r=3-1
r=2
in percentage
r=200%
is a rate of growth, because the value of b is greater than 1
In this problem, we have a exponential function, because the y-values have equal ratios
Verify
9/3=3
27/9=3
81/27=3
243/81=3
therefore
the answers are
Part a
we have a exponential function, because the y-values have equal ratios
Part b
the rate of growth is 200% or 2
Part c
the equation is y=3^x