Question

this table shows several values of an exponential function.
x | f(x)
0 | 7
1 | 21
2 | 63
3 | 189
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 \( x = 0 \), \( f(0)=a(b)^0=a\times1 = a \). From the table, when \( x = 0 \), \( f(0)=7 \), so \( a = 7 \).

Step2: Find the value of \( b \)

We know \( a = 7 \), so the function is \( f(x)=7(b)^x \). Now use another point, say \( x = 1 \), \( f(1)=21 \). Substitute into the function: \( 21=7(b)^1 \). Solve for \( b \): divide both sides by 7, \( \frac{21}{7}=b \), so \( b = 3 \).

Step3: Write the function

Now that we have \( a = 7 \) and \( b = 3 \), the function is \( f(x)=7(3)^x \).

Answer:

\( f(x) = 7(3)^x \)