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graph of $y=5(1.2)^x$ is shown in the $-$ plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation as written?

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Find derivatives using logarithmic differentiation

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Q. graph of

y=5(1.2)^x

is shown in the

-

plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation as written?

Identify Equation Components: The equation given is $y=5(1.2)^x$ . To understand the characteristics of the graph that are displayed as constants or coefficients, we need to identify each part of the equation and its role in the graph. $\newline$ The number $5$ is the initial value or the $y$ -intercept of the graph when $x=0$ . This is because when $x=0$ , $y=5(1.2)^0$ , and anything raised to the power of $0$ is $1$ , so $y=5\times1$ , which is $5$ .
Interpret Initial Value: The number $1.2$ is the base of the exponential function. This base represents the growth factor per unit increase in $x$ . Since the base is greater than $1$ , it indicates that the graph represents exponential growth.
Understand Base Role: The variable $x$ is the exponent in the equation, which represents the independent variable on the horizontal axis of the graph. The value of $y$ depends on the value of $x$ , and as $x$ increases, $y$ increases exponentially because of the base $1.2$ .
Explain Variable $x$ : The constant $5$ and the coefficient $1.2$ are explicitly shown in the equation. The constant $5$ is the $y$ -intercept, and the coefficient $1.2$ is the growth factor of the exponential function.

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