Answer:
The function is an exponential,
f(x) = A exp(log(3)x) = 2×3^x = 2(3)^x
The first point you graph for any exponential is (0,A), here (0,2). After (1,6), the next point might be (2,18).
Step-by-step explanation:
(0,2×3^0) = (0,2)
(1,2×3^1) = (1,6)
(2,2×3^2) = (2,2×9) = (2,18)
2(3)^x ought to be written 2×3^x, that is, two times three raised to the x power. x can be any real number.
Since 3 = exp(log(3)), we can substitute for 3 and write 2×exp(log(3))^x. Since exp(p)^q = exp(p×q), the function is also written 2×exp(log(3)x).
exp(x) is also written e^x. exp(x) is the unique function with exp(0)=1, and with the slope of the tangent line at exp(x) equal to exp(x). For instance, the slope at exp(0) is 1, the slope at exp(1) = e is e, slope at exp(2) is exp(2).
for A exp(b x), the slope at x is A b exp(b x).
For 3^x = exp(log(3)x), we have
3^0=1, slope log(3)
3^1=3, slope 3log(3),
3^2=9, slope 9log(3).
