Find an equation of the tangent line at the point indicated....

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Key Concepts

Differentiation of Exponential Functions

Differentiating exponential functions involves applying the rule that the derivative of a^x is a^x multiplied by the natural logarithm of the base (ln(a)). This rule enables one to compute how rapidly exponential functions change, which is essential when determining the slope of the tangent line at any point on the curve.

Tangent Line

A tangent line to a curve at a particular point is a straight line that touches the curve exactly at that point and shares the same slope as the curve does at the point. It serves as a linear approximation to the function near that point, making it useful for estimating function values locally.

Exponential Functions

Exponential functions are functions where a constant base is raised to a variable exponent. They are fundamental in describing growth and decay processes and have unique properties such as a constant relative rate of change, which are valuable in various fields of study.

Derivative

The derivative of a function measures the instantaneous rate of change of the function with respect to its input. In the context of calculus, it is used to determine the slope of the tangent line to the curve at any given point, providing essential information for analyzing the behavior of functions.

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