Question

x

f(x)

----

----

-2

5

0

15

2

45

4

multipliery-interceptequation

Explanation:

Step1: Identify the multiplier (ratio)

Check the ratio of consecutive $f(x)$ values when $x$ increases by 2:
$\frac{15}{5}=3$, $\frac{45}{15}=3$

Step2: Confirm exponential model form

The general form is $f(x)=a(b)^{\frac{x}{h}}$, where $h=2$ (interval of $x$), $b=3$ (multiplier). Use $x=0, f(x)=15$ to find $a$:
$15=a(3)^{\frac{0}{2}} \implies a=15$

Step3: Find $f(4)$

Substitute $x=4$ into the equation:
$f(4)=15(3)^{\frac{4}{2}}=15(3)^2=15\times9=135$

Step4: State y-intercept

The y-intercept is $f(0)=15$

Step5: Write the final equation

Substitute $a=15$, $b=3$, $h=2$ into the model:
$f(x)=15(3)^{\frac{x}{2}}$

Answer:

• $f(4)=135$
• Multiplier: $3$
• Y-intercept: $15$
• Equation: $f(x)=15(3)^{\frac{x}{2}}$