Question

The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive.

A 2-column table with 6 rows. The first column is labeled number of days with entries 0, 10, 20, 30, 40, 50. The second column is labeled estimated number of bees with entries 10,000; 7,500; 5,600; 4,200; 3,200; 2,400.
Which function best models the data?

y = 9,958(0.972)x
y = 0.972(9,958)x
y = 9,219x– 150
y = –150x + 9,219

Answer 1

To determine which function best models the data, we can first look at the pattern in the decrease in the number of bees as the days increase.

By looking at the data, the number of bees is decreasing with each increase in days. This suggests that the function should involve a negative slope or a negative coefficient for the x variable.

Looking at the provided functions:
1. y = 9,958(0.972)^x
2. y = 0.972(9,958)^x
3. y = 9,219x - 150
4. y = -150x + 9,219

Based on the pattern observed in the data and the given functions, the most appropriate function that models the data is:
4. y = -150x + 9,219

This function has a negative coefficient for x and closely reflects the decreasing trend in the number of bees as the days progress.