Question

the table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive. bee population over time number of days estimated number of bees 0 10,000 10 7,500 20 5,600 30 4,200 40 3,200 50 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

Explanation:

Step1: Check the form of the function

The data shows a decreasing trend. The general form of an exponential function is \(y = a(b)^{x}\), where \(a\) is the initial value and \(b\) is the base (\(0 < b< 1\) for decay). A linear function is \(y=mx + c\).

Step2: Test the exponential function \(y = 9958(0.972)^{x}\)

When \(x = 0\), \(y=9958(0.972)^{0}=9958\times1 = 9958\approx10000\) (due to rounding in the model).
For a linear function \(y=- 150x + 9219\), when \(x = 0\), \(y = 9219
eq10000\). For \(y = 9219x-150\), when \(x = 0\), \(y=-150
eq10000\). For \(y = 0.972(9958)^{x}\), when \(x = 0\), \(y = 0.972
eq10000\).

Answer:

\(y = 9958(0.972)^{x}\)