How is an exponential function different from a polynomial function? Use specific examples to illustrate your points. Discuss the number of possible zeros, the behavior of the graphs, and possible real-world examples for each.

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10-12-2017
Mathematics

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How is an exponential function different from a polynomial function? Use specific examples to illustrate your points. Discuss the number of possible zeros, the behavior of the graphs, and possible real-world examples for each.

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KOA1234 KOA1234 · Answer 1 · 2017-12-10T05:09:45+01:00

Polynomial: x is at the base that can be raised to a constant power
Expo: "X" IS the exponent.

Polynomial: Number of zeroes is based on the power of "x" in the leading term
Example : 3x^2 +2x+2 - "3x^2 is the leading term. It has to zeroes because x is raised to the power 2
Exponential: Technically only has one.

Polynomial: It's wavy in appearance with positive and negative slopes.
Exponential: Almost "L" shaped in appearance with slopes going in one direction (positive or negative) that starts from almost flashing from one part of the "L" to almost flashing with the other side.

Polynomial: Rollercoaster tracks
Exponential: Rabbits' population grows 200% each year.

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MrRoyal MrRoyal · Answer 2 · 2021-11-20T12:50:41+01:00

A polynomial function and an exponential function are illustrations of the function model.

(a) The base and exponents

The base of a polynomial function is a variable, and its exponent is a constant, while the exponent of an exponential function is a variable.

(b) The roots

The number of roots of a polynomial function is the degree of the function, while an exponential function has one root.

(c) Examples

Polynomials are used in buildings and constructions; e.g. the rollercoaster tracks, while exponential functions are used to model populations

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