use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for…

use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for x. based on your graph, describe the shape of a scatter plot that can be modeled by ( f(x)=b^{x},0 < b < 1 ).\n( f(x)=left(\frac{1}{7}\right)^{x} )\nbelow.\na. increasing more and more rapidly\nb. decreasing more and more rapidly\nc. increasing, with the rate of increase slowing down\nd. decreasing, with the rate of decrease slowing down\ne. decreasing and then increasing\nf. increasing and then decreasing

use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for x. based on your graph, describe the shape of a scatter plot that can be modeled by ( f(x)=b^{x},0 < b < 1 ).\n( f(x)=left(\frac{1}{7}\right)^{x} )\nbelow.\na. increasing more and more rapidly\nb. decreasing more and more rapidly\nc. increasing, with the rate of increase slowing down\nd. decreasing, with the rate of decrease slowing down\ne. decreasing and then increasing\nf. increasing and then decreasing

Answer

Explanation:

Step1: Calculate function values

When (x = - 2), (f(-2)=\left(\frac{1}{7}\right)^{-2}=7^{2} = 49) When (x=-1), (f(-1)=\left(\frac{1}{7}\right)^{-1}=7^{1}=7) When (x = 0), (f(0)=\left(\frac{1}{7}\right)^{0}=1) When (x = 1), (f(1)=\left(\frac{1}{7}\right)^{1}=\frac{1}{7}) When (x = 2), (f(2)=\left(\frac{1}{7}\right)^{2}=\frac{1}{49})

Step2: Analyze the trend

As (x) increases ((-2\to - 1\to0\to1\to2)), the function values (49\to7\to1\to\frac{1}{7}\to\frac{1}{49}) are decreasing. The general form of an exponential function (y = b^{x}), when (0 < b<1), is a decreasing function. The rate of decrease is such that as (x) gets larger, the function approaches (0) but the rate at which it decreases slows down (since the ratio of consecutive function values (\frac{f(x + 1)}{f(x)}=b) and (0 < b<1)).

Answer:

D. Decreasing, with the rate of decrease slowing down