Question

Drag each number to the correct location on the table. Each number can be used more than once, but not all numbers will be used.Consider exponential functions fg and h defined by the tables below. Complete each table.64 24 36 32 3020Xf(x)g(x)Xh(x)1112216238348doNextentum.com/assessments-delivery/ua/mt/launch/./aHR0cHM6Ly9mMSShcHAUZWRtZW5odWouY29tL2x/YXJuZXItdWkvc2VJb25kYXJSL3VzZXItYXNzaWdubW412X123

Answer 1

Since f is an exponential function, it follows that there are some constants a and b such that:

$f(x)=ab^x$

Therefore,

$f(1)=ab=4$$f(2)=ab^2=12$

Hence,

$\begin{gathered} \frac{ab^2}{ab}=\frac{12}{4}=3 \\ b=3 \end{gathered}$

Therefore,

$\begin{gathered} 3a=4 \\ a=\frac{4}{3} \end{gathered}$

Hence, the function f is given by:

$\begin{gathered} f(x)=\frac{4}{3}\times3^x \\ f(x)=4\cdot3^{x-1} \end{gathered}$

Substitute x = 3 into the function:

$f(3)=4\cdot3^{3-1}=4\cdot3^2=36$