Question

write a function that models the data.

x	y
1	150
2	90
3	54
4	32.4

$y = \square$

Explanation:

Step1: Check if it's exponential

Calculate the ratios of consecutive y - values.
$\frac{150}{250} = 0.6$, $\frac{90}{150}=0.6$, $\frac{54}{90} = 0.6$, $\frac{32.4}{54}=0.6$. The common ratio \( r = 0.6 \).

Step2: Identify the form of exponential function

The general form of an exponential function is \( y = a\cdot r^{x} \), where \( a \) is the initial value (when \( x = 0 \)). When \( x = 0 \), \( y=250 \), so \( a = 250 \) and \( r=0.6 \).
So the function is \( y = 250\cdot(0.6)^{x} \).

Answer:

\( y = 250(0.6)^x \)