SOLUTION: The graph of the exponential function f(x) is shown below. Find f(x). The graph passes through the points (0,3) and (1,6).

Algebra ->  Functions -> SOLUTION: The graph of the exponential function f(x) is shown below. Find f(x). The graph passes through the points (0,3) and (1,6).      Log On


   

Question 1209343: The graph of the exponential function f(x) is shown below. Find f(x).
The graph passes through the points (0,3) and (1,6).
Found 2 solutions by mccravyedwin, math_tutor2020:
Answer by mccravyedwin(407) About Me  (Show Source):
Answer by math_tutor2020(3817) About Me  (Show Source):
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Plug in the coordinates of (0,3)
y = a*b^x
3 = a*b^0
3 = a*1
a = 3

Now plug in (1,6)
y = a*b^x
y = 3*b^x
6 = 3*b^1
6 = 3*b
b = 6/3
b = 2

a = 3 and b = 2 has y = a*b^x update to y = 3*2^x

Check:
Let's plug in x = 0
y = 3*2^x
y = 3*2^0
y = 3*1
y = 3
This shows that (0,3) is on the curve.
Now try x = 1
y = 3*2^x
y = 3*2^1
y = 3*2
y = 6
(1,6) is also on the curve.
The exponential equation is confirmed.


Answer: f(x) = 3*2^x