Question

Exponential functions over unit intervals 2YT How does f(x)=2*0.15ˣ change over the interval from x=-3 to x=-2?

Answer 1

Over the interval from x=-3 to x=-2, the function f(x)=2*0.15ˣ decreases.

Step-by-step explanation:

To understand how the function f(x)=2*0.15ˣ changes over the interval from x=-3 to x=-2, let's analyze its behavior. The function is an exponential function of the form f(x)=a*bˣ, where a is the initial value and b is the base. In this case, a=2 and b=0.15.

Starting with x=-3, we can calculate the function value:

`\[ f(-3) = 2 * 0.15^(-3) \]`

And for x=-2:

`\[ f(-2) = 2 * 0.15^(-2) \]`

Comparing these two values, we observe that as x increases from -3 to -2, the exponent becomes less negative, resulting in a larger denominator for the fraction 0.15ˣ. Since the base is between 0 and 1, raising it to a less negative power leads to an increase in the overall value. Therefore, f(x) decreases over the specified interval.

Understanding the behavior of exponential functions in terms of their base and exponent is crucial for analyzing their trends over intervals