Question

Consider the three exponential functions f(x)=a⋅bxf(x)=a⋅bx, in red, g(x)=c⋅dxg(x)=c⋅dx, in blue, and h(x)=p⋅qxh(x)=p⋅qx, in green, graphed below where a,b,c,d,p,qa,b,c,d,p,q are constants.

For each statement below, enter all of the possible constants (letters a, b, c, d, p, or q) as a list of letters in any order without any separating commas. For example a possible answer could be apdq which is equivalent to paqd (or any other order of these four constants), but a, d, p, q would not be graded correctly because it includes commas.
(c) Which of these constants could possibly be between 0 and 1?

Answer 1

In exponential functions, the constants that can be between 0 and 1 are a, c, and p.

Step-by-step explanation:

The exponential functions f(x)=a x bˣ, g(x)=c x dˣ, and h(x)=p x qˣ can have constants between 0 and 1. Let's look at each constant individually:

The constant a can be any value between 0 and 1, inclusive.

The constant b must be greater than 1 for the function to be exponential.

The constant c can be any value between 0 and 1, inclusive.

The constant d must be greater than 1 for the function to be exponential.

The constant p can be any value between 0 and 1, inclusive.

The constant q must be greater than 1 for the function to be exponential.

Answer 2

The constants b, d, and q from the exponential functions f(x), g(x), and h(x) respectively could be between 0 and 1, indicating exponential decay.

Step-by-step explanation:

The question relates to understanding the properties of exponential functions and their constants. For the exponential functions f(x)=a ⋅ b^x, g(x)=c ⋅ d^x, and h(x)=p ⋅ q^x, the constants that could possibly be between 0 and 1 are b, d, and q.

This is because if the base of an exponential function is between 0 and 1, the function represents exponential decay, where the graph of the function decreases as x increases.

Therefore, if the graphs indicate an exponential decrease, the respective bases must be between 0 and 1.