Question

this table shows several values of an exponential function. x | f(x) -2 | 1 -1 | 2 0 | 4 1 | 8 2 | 16 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 \( x = 0 \), \( f(0) = 4 \). So, \( a = 4 \).

Step2: Find the value of \( b \)

Now that we know \( a = 4 \), the function is \( f(x)=4(b)^x \). Let's use another point from the table, say \( x = 1 \), \( f(1)=8 \). Substitute into the function: \( 8 = 4(b)^1 \).
Simplify the equation: \( 8 = 4b \). Divide both sides by 4: \( b=\frac{8}{4}=2 \).

Answer:

\( f(x) = 4(2)^x \)