Question

Identify whether the set of ordered pairs represent an exponential function. Explain your answer. (1,-7) (2,-14), (3,14) (4,7)

Answer 1

EXPLANATION :

From the problem, we have the points :

`(1,-7),(2,-14),(3,14),(4,7)`

The points represent an exponential function if all points satisfy the equation in the form :

`y=ab^x`

Let's try (1, -7)

`\begin{gathered} -7=ab^1 \\ ab=-7 \end{gathered}`

(2, -14)

`\begin{gathered} -14=ab^2 \\ -14=ab(b) \\ \text{ Note that ab = -7 from the first equation :} \\ -14=-7b \\ b=(-14)/(-7)=2 \end{gathered}`

We have b = 2.

Using the first equation, solve for a :

`\begin{gathered} ab=-7 \\ 2a=-7 \\ a=-(7)/(2) \end{gathered}`

So the equation now will be :

`\begin{gathered} y=ab^x \\ y=-(7)/(2)(2)^x \end{gathered}`

Let's check the third and fourth points, they must satisfy the equation :

`\begin{gathered} \text{ For \lparen3, 14\rparen} \\ 14=-(7)/(2)(2)^3 \\ 14=-(7)/(2)(8) \\ 14=-28 \\ 14=-28 \\ \text{ False!} \end{gathered}`

Since the third point does NOT satisfy the equation, therefore, this is NOT an exponential function