Consider the three exponential functions \( f(x) = a \cdot b^x \) in red, \( g(x) = c \cdot d^x \) in blue, and \( h(x) = p \cdot q^x \) in green, graphed below where \( a, b, c, d, p, q \) 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 pagd (or any other order of these four constants), but a, d, p, q would not be graded correctly because it includes commas.(a) Which of these constants are definitely positive? [Answer box](b) Which of these constants are definitely greater than 1? [Answer box](c) Which of these constants could possibly be between 0 and 1? [Answer box](d) Which of these constants could possibly be greater than the value of c? [Answer box](e) Which two of these constants are definitely equal? [Answer box]### Graph Description:The graph displays three curves, each corresponding to one of the given functions:- The red curve represents \( f(x) = a \cdot b^x \). It shows exponential growth, increasing from left to right.- The blue curve represents \( g(x) = c \cdot d^x \). It appears to show exponential decay, decreasing from left to right.- The green curve represents \( h(x) = p \cdot q^x \). It shows another type of exponential decay, also decreasing from left to right.The graphical intersection and relative positioning of these curves help in answering the questions regarding the constants \( a, b, c, d, p, \) and \( q \).

Given thatf(x) = a.bxg(x) = c.dxh(x)= p.qxAlso the graph of f(x),g(x),h(x) are provided in the…

Consider the three exponential functions f(x) = a - b, in red, g(z)=c-d, in blue, and h(z) - p-q², in green, graphed below where a, 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. (a) Which of these constants are definitely positive? (b) Which of these constants are definitely greater than 1? (c) Which of these constants could possibly be between 0 and 1? (d) Which of these constants could possibly be greater than the value of ? (e) Which two of these constants are definitely equal? 1. f(x)=(b)^x/ X g(x)(d)^x h(x)#p(q)x

Consider the three exponential functions f(x) = a - b, in red, g(z)=c-d, in blue, and h(z) - p-q², in green, graphed below where a, 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. (a) Which of these constants are definitely positive? (b) Which of these constants are definitely greater than 1? (c) Which of these constants could possibly be between 0 and 1? (d) Which of these constants could possibly be greater than the value of ? (e) Which two of these constants are definitely equal? 1. f(x)=(b)^x/ X g(x)(d)^x h(x)#p(q)x

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the three exponential functions \( f(x) = a \cdot b^x \) in red, \( g(x) = c \cdot d^x \) in blue, and \( h(x) = p \cdot q^x \) in green, graphed below where \( a, b, c, d, p, q \) 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 pagd (or any other order of these four constants), but a, d, p, q would not be graded correctly because it includes commas.

(a) Which of these constants are definitely positive?
[Answer box]

(b) Which of these constants are definitely greater than 1?
[Answer box]

(c) Which of these constants could possibly be between 0 and 1?
[Answer box]

(d) Which of these constants could possibly be greater than the value of c?
[Answer box]

(e) Which two of these constants are definitely equal?
[Answer box]

### Graph Description:
The graph displays three curves, each corresponding to one of the given functions:

- The red curve represents \( f(x) = a \cdot b^x \). It shows exponential growth, increasing from left to right.
- The blue curve represents \( g(x) = c \cdot d^x \). It appears to show exponential decay, decreasing from left to right.
- The green curve represents \( h(x) = p \cdot q^x \). It shows another type of exponential decay, also decreasing from left to right.

The graphical intersection and relative positioning of these curves help in answering the questions regarding the constants \( a, b, c, d, p, \) and \( q \).

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