Rewrite the Equation in Terms of Base E $$y = 400 ( 3.8 ) ^ { x }$$

question 199

Multiple Choice

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three
decimal places.
- $$y = 400 ( 3.8 ) ^ { x }$$

• A) \(y = 400 \mathrm { e } ^ { x \ln 3.8 } , \mathrm { y } = 400 \mathrm { e } ^ { 1.335 \mathrm { x } }\)
• B) \(y = 3.8 \mathrm { e } ^ { x } \ln 400 , y = 3.8 \mathrm { e } ^ { 5.991 x }\)
• C) \(\mathrm { y } = 400 \mathrm { e } ^ { 3.8 \mathrm { x } } , \mathrm { y } = 4002.718 ^ { 1.335 \mathrm { x } }\)

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Definitions:

Earth Care

A philosophy or practice of taking actions to preserve and protect the environment and the planet's ecosystems.

Deep Ecology

An environmental philosophy and social movement emphasizing the inherent worth of all living beings regardless of their instrumental utility to human needs.

Interdependence

The mutual reliance between different species, systems, or processes in an ecosystem, illustrating how a change in one can affect others.

Fundamental Ecosystems

Basic ecological units comprised of living organisms and their physical environment, interacting as a system.