You have the following expression for an exponential function:
![f(x)=a(b)^x](https://img.qammunity.org/qa-images/2023/formulas/mathematics/high-school/lis6vvsvswr4cmmxqy4f.png)
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)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/8je8u3e1vinph2774jo5.png)
and the second pair (-1,8) means that for x=-1, f(x)=8:
![8=a(b)^(-1)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/jnaznef96osh2e3bb6gq.png)
If you divide the second equation between the first equation, you can cancel out coefficient a and solve for b:
![\begin{gathered} (8)/(4)=(a(b)^(-1))/(a(b)^(-2)) \\ 2=(b)^(-1)(b)^2 \\ 2=(b)^(-1+2) \\ 2=b \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/zhlpih67g1bjjn4b2nlu.png)
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=(a)/((2)^2) \\ 4=(a)/(4) \\ 16=a \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/61es9sd3a2em112pmr8y.png)
Hence, the form of the function f(x) is:
![f(x)=16(4)^x](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/537fv7f1x3hfs0lah4o3.png)