Answer: 12
Step-by-step explanation
An exponential function is in the form y = f(x) = a · b^x
Given,
When x = 0, y = 3
When x = 1, y = 6
Therefore,
Since y = a · b^x
When x = 0, y = 3
3 = a(b^0)
Any value raised to the power of 0 = 1
Therefore a = 3
So the exponential function we are considering is rewritten as y = f(x) = 3 · b^x
Since y = 3 · b^x
When x = 1, y = 6
6 = 3 · b^1
6 = 3b
3b = 6
Divide both sides of the equation by 3
3b/3 = 6/3
b = 2
So the exponential function we are considering is rewritten as y = f(x) = 3 · 2^x
When x =2, y = r
To find the value of r
y = f(x) = 3 · 2^x
r = 3 · 2^2
r = 3 · 4
r = 12
Therefore, the value of r that will make the table a representation of an exponential function is 12