Question

Identify which of the twelve basic functions listed below fit the description given.

The one function that is decreasing (0,c).
a) y=x
b) y=1+e−x
c) y=ln⁡x
d) y=1

Answer 1

Function b) y=1+e^-x is the exponential decay function that fits the description of decreasing on the interval (0, c).

Step-by-step explanation:

To identify which of the twelve basic functions fits the description of decreasing on the interval (0, c), let's examine the options provided:

• a) y=x - This is a linear function with a constant slope of 1. It's neither decreasing nor increasing on the interval (0, c) as the slope is positive everywhere.
• b) y=1+e-x - This is an exponential decay function. Since the exponent has a negative sign, the function is decreasing on the interval (0, c).
• c) y=ln(x) - The natural logarithm function is increasing as x increases, so it does not fit the description.
• d) y=1 - This is a constant function and does not change; therefore, it is neither increasing nor decreasing.

Based on the analysis, b) y=1+e-x is the function that is decreasing on the interval (0, c).