Question

write a function that models the data.

x	y
1	150
2	90
3	54
4	32.4

y = \square

Explanation:

Step1: Check for exponential model

We suspect an exponential function of the form \( y = ab^x \). When \( x = 0 \), \( y = 250 \), so \( a = 250 \) (since \( y = 250b^0 = 250 \times 1 = 250 \)).

Step2: Find the common ratio \( b \)

Calculate the ratio of consecutive \( y \)-values:

• \( \frac{150}{250} = 0.6 \)
• \( \frac{90}{150} = 0.6 \)
• \( \frac{54}{90} = 0.6 \)
• \( \frac{32.4}{54} = 0.6 \)

So \( b = 0.6 \).

Step3: Write the function

Substitute \( a = 250 \) and \( b = 0.6 \) into \( y = ab^x \), we get \( y = 250(0.6)^x \).

Answer:

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