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

y = 9,958(0.972)^x

Reason: at x = 0 the population is about 10,000, so a model with initial value ≈9,958 fits. Also 9,958(0.972)^10 ≈ 9,958·0.753 ≈ 7,500, matching the day-10 value, so the exponential decay model fits the data. The other forms give incorrect initial values or unrealistic growth/decline.