Exponential Functions

We want to identify the value of the base of the exponential function from the given graph.

Let's consider the given equation for this graph.

y = b^{x}

Let's first substitute the given point which has

1

as its

x -

coordinate into the above formula. This will allow us to find the value of

b .

Let's substitute

(1, 3)

into the above formula.

y = b^{x}

x = 1

,

y = 3

3 = b^{1}

Solve for

b

a^{1} = a

3 = b

RearrangeEqnRearrange equation

b = 3

Now we can write our equation.

y = b^{x} \Rightarrow y = 3^{x}

Next, we will substitute other given points,

(0, 1)

and

(- 1, \frac{1}{3}),

into the above equation to check it. Let's start from

(0, 1) .

y = 3^{x}

x = 0

,

y = 1

1 = 3^{0}

a^{0} = 1

1 = 1

The second point satisfies the equation. Let's try the last one,

(- 1, \frac{1}{3}) .

y = 3^{x}

x = - 1

,

y = \frac{1}{3}

\frac{1}{3} = 3^{- 1}

a^{- m} = \frac{1}{a ^{m}}

\frac{1}{3} = \frac{1}{3 ^{1}}

a^{1} = a

\frac{1}{3} = \frac{1}{3}

All the given points satisfy the equation. Now we can be sure that

b = 3 .

Exponential Functions 1.1 - Solution