30.3k views
4 votes
Identify whether the set of ordered pairs represent an exponential function. Explain your answer. (1,-7) (2,-14), (3,14) (4,7)

User JDR
by
7.5k points

1 Answer

1 vote

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

User Brenda
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.