Question

The table of ordered pairs gives an exponential function.

Write an equation for the function. NEED ASAP!!!

Answer 1

`y=4\cdot \left((1)/(3)\right)^x`

Explanation:

The general form of an exponential function is:

`\boxed{\begin{array}{l}\underline{\textsf{General form of an Exponential Function}}\\\\\large\text{$f(x)=a\cdot b^x$}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ is the initial value ($y$-intercept).}\\ \phantom{ww}\bullet\;\textsf{$b$ is the base (growth/decay factor) in decimal form.}\end{array}}`

The y-intercept is the point at which a graph intersects the y-axis, so where the x-coordinate is zero. Therefore, to find the initial value (a) from the given table of values, identify the y-value that corresponds to x = 0. So:

`a = 4`

As the x-values in the table increase by a constant value of one, to find the base (b) of the exponential function, we divide a y-value by the preceding y-value:

`b=(4)/(12)=(1)/(3)`

Therefore, the equation of the exponential function that models the given table of values is:

`\large\boxed{\boxed{y=4\cdot \left((1)/(3)\right)^x}}`