Question

this table shows several values of an exponential function.
x | f(x)
1 | -9
2 | -27
3 | -81
4 | -243
write an equation for the function in the form f(x) = a(b)^x.
use whole numbers, decimals, or simplified fractions for the values of a and b.
f(x) =
submit

Explanation:

Step1: Find base $b$

Divide consecutive $f(x)$ values:
$\frac{f(2)}{f(1)} = \frac{-27}{-9} = 3$, $\frac{f(3)}{f(2)} = \frac{-81}{-27} = 3$, so $b=3$.

Step2: Solve for $a$

Substitute $x=1$, $f(1)=-9$, $b=3$ into $f(x)=a(b)^x$:
$-9 = a(3)^1$
Solve for $a$: $a = \frac{-9}{3} = -3$

Step3: Build the function

Substitute $a=-3$ and $b=3$ into the form.

Answer:

$f(x) = -3(3)^x$