Question

Which function best models the data?

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
O y = 9,958(0.972)*
y = 0.972(9,958)*
O y = 9,219x, 150
O y = -150x + 9,219
Number of days
0
10
20
30
40
50
Estimated number of bees
10.000
7.500
5.600
4,200
3,200
2.400

Answer 1

y=9,958(0.972)^x...................

Answer 2

y = 9,958(0.972)^t

Explanation:

From point to point, the difference in days is always constant (10 days), but the difference between estimated number of bees is not constant.

10000 - 7500 = 2500

7500 - 5600 = 1900

5600 - 4200 = 1600

4200 - 3200 = 1000

3200 - 2400 = 800

Therefore, the data don't fit a line.

From the other two options:

y = 9,958(0.972)^t

y = 0.972(9,958)^t

only the first one has sense, because its initial amount of bees is 9,958 (near to 10,000) and in the second option is 0.972.