Question

Enter an equation for the function that includes the points. Give your answer in the form a (bx). In theevent that a = 1, give your answer in the form bx(-2,4) and (-1,8)The equation is f(x)=

Answer 1

You have the following expression for an exponential function:

$f(x)=a(b)^x$

By using the given points (-2,4) and (-1,8), you can find the values of coeffcients a and b, as follow:

The first pair (-2,4) means that for x=-2, f(x)=4:

$4=a(b)^{-2}$

and the second pair (-1,8) means that for x=-1, f(x)=8:

$8=a(b)^{-1}$

If you divide the second equation between the first equation, you can cancel out coefficient a and solve for b:

$\begin{gathered} \frac{8}{4}=\frac{a(b)^{-1}}{a(b)^{-2}} \\ 2=(b)^{-1}(b)^2 \\ 2=(b)^{-1+2} \\ 2=b \end{gathered}$

where you have used properties of exponents.

Now, if you replace the previous value of b into any of the equations for the pairs, for instance, into the first equation, you obtain for a:

$\begin{gathered} 4=a(2)^{-2} \\ 4=\frac{a}{(2)^2} \\ 4=\frac{a}{4} \\ 16=a \end{gathered}$

Hence, the form of the function f(x) is:

$f(x)=16(4)^x$