Question

Consider the table below

Answer 1

Answer: 12

 

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