Question

Find the equation of the exponential function represented by the table below:

Answer 1

Answer:

$f(x)=5(4)^x$

Step-by-step explanation:

The exponential function is $f(x)=ab^x$.  $a$ is the initial value of the function, or the y-value when x=0. In this case, $a$=5. If we enter that into the equation:

$f(x)=5b^x$

Then we can use another point to solve for $b$.

$20=5b^1$

Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.

$20=5b\\\frac{20}{5}=\frac{5b}{5}\\b=4$

Now that we have both the $a$ and $b$ value, we can return to the exponential function and fill in the blanks.

$f(x)=5(4)^x$

I hope this helps!