Question

The table of ordered pairs (x, y) gives an exponential function.

Write an equation for the function.
y
- 1
6
0
12
1
24
2
48

Answer 1

f(x) = 12*(2)^x

Explanation:

A generic exponential equation is written as:

f(x) = A*(r)^x

And we also know that this equation passes through:

(-1, 6)

(0, 12)

(1, 24)

(2, 48)

For the second point, (0, 12) we know that when f(0) = 12

Then:

f(0) = 12 = A*(r)^0

And for every real number different than zero, a^0 = 1

Then:

f(0) = A*1 = A = 12

Then the equation is:

f(x) = 12*(r)^x

Now we can use one of the other points, like (1, 24)

Then f(1) = 24

We can solve:

f(1) = 24 = 12*(r)^1 = 12*r

24/12 = r

2 = r

Then the equation is f(x) = 12*(2)^x

Now we need to check if this function also passes through the points (-1, 6) and (2, 24):

f(-1) = 12*(2)^-1 = 12/2 = 6

f(2) = 12*(2)^2 = 12*4 = 48

Nice.

So we can see that the function is f(x) = 12*(2)^x