Question

the height, p(x) in feet, of the water level in a lake, for a given number of days, x, is shown in the table.

x	1	2	3	4
p(x)	3	12	48	192

does the exponential function p(x) represent growth or decay? why?

• it shows decay because as x increases, p(x) grows away from 0
• it shows decay because as x increases, p(x) gets closer to 0
• it shows growth because as x increases, p(x) grows away from 0
• it shows growth because as x increases, p(x) gets closer to 0

Explanation:

To determine if \( p(x) \) is growth or decay, we analyze the table. As \( x \) (days) increases from 1 to 4, \( p(x) \) (water level) goes from 3 to 12 to 48 to 192. This means \( p(x) \) is increasing (growing) and moving away from 0. Decay would involve \( p(x) \) decreasing toward 0, which is not the case here. So the correct reasoning is that it shows growth because as \( x \) increases, \( p(x) \) grows away from 0.

Answer:

It shows growth because as \( x \) increases, \( p(x) \) grows away from 0