Question

this table shows several values of an exponential function.
x | f(x)
0 | -2
1 | -14
2 | -98
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) =

Explanation:

Step1: Find the value of \( a \)

For an exponential function \( f(x) = a(b)^x \), when \( x = 0 \), \( f(0)=a(b)^0=a(1)=a \). From the table, when \( x = 0 \), \( f(0)=-2 \), so \( a=-2 \).

Step2: Find the value of \( b \)

We know \( a = -2 \), and when \( x = 1 \), \( f(1)=-14 \). Substitute into the function: \( -14=-2(b)^1 \). Solve for \( b \): divide both sides by -2, \( b=\frac{-14}{-2}=7 \). We can check with \( x = 2 \): \( f(2)=-2(7)^2=-2\times49=-98 \), which matches the table.

Answer:

\( f(x)=-2(7)^x \)