Question

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

$x$	$f(x)$

a - value: ____________

b - value: ____________

growth/decay? why? __________________________

Explanation:

Step1: Identify a-value (initial term)

The general exponential form is $f(x)=a \cdot b^x$. For $f(x)=3^x$, this is $f(x)=1 \cdot 3^x$, so $a=1$.

Step2: Identify b-value (base)

From $f(x)=1 \cdot 3^x$, the base $b=3$.

Step3: Determine growth/decay rule

Exponential growth occurs when $b>1$; decay when $01$.

Step4: Calculate table values

Choose $x=-2,-1,0,1,2$:

• $x=-2$: $f(-2)=3^{-2}=\frac{1}{3^2}=\frac{1}{9}\approx0.11$
• $x=-1$: $f(-1)=3^{-1}=\frac{1}{3}\approx0.33$
• $x=0$: $f(0)=3^{0}=1$
• $x=1$: $f(1)=3^{1}=3$
• $x=2$: $f(2)=3^{2}=9$

Answer:

Table of Values:

$x$	$f(x)$
$-1$	$\frac{1}{3}\approx0.33$
$0$	$1$
$1$	$3$
$2$	$9$

Key Values & Classification:

a-value: $1$
b-value: $3$
Growth/decay? WHY? Growth, because the base $b=3>1$

(Graph instructions: Plot the points from the table, draw a smooth curve that increases from left to right, approaches the x-axis (y=0) as $x\to-\infty$, and rises rapidly as $x$ increases.)