An exponential function of form f left parenthesis x right parenthesis equals b Superscript x includes the points​ (2, 16),​ (3, 64), and​ (4, 256). What is the value of​ b?

Question

solve for b

Answer 1

Each point is an ordered pair consisting of an "x" and a "y" in the form (x, y) so you can plug in the "x" and "y" into the equation:

f(x) = b^x or y = b^x (since "f(x)" is the same as "y")

For (2, 16) then:

16 = b² or b = ±4

For (3, 64) then:

64 = b³ or b = 4

For (4, 256) then:

256 = b⁴ or b = ±4

b = 4 is the only solution that works for all three points

Answer 2

f(2) = 16 = 4²

f(3) = 64 = 4³

f(4) = 256 = 4⁴

f(x) = b^x = 4^x

So, b = 4.