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If
y=30((9)/(10))^(x) is graphed in the
xy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
Choose 1 answer:
(A) Slope
(B) The value
y approaches as
x decreases
(C)
x-intercept
(D)
y-intercept

If $y=30\left(\frac{9}{10}\right)^{x}$ is graphed in the $x y$ -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation? $\newline$ Choose $1$ answer: $\newline$ (A) Slope $\newline$ B The value $y$ approaches as $x$ decreases $\newline$ (C) $x$ -intercept $\newline$ (D) $y$ -intercept

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View step-by-step help

Inverses of csc, sec, and cot

Full solution

Q. If

y=30\left(\frac{9}{10}\right)^{x}

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

Choose

1

answer:

\newline

(A) Slope

\newline

B The value

y

approaches as

x

decreases

\newline

(C)

x

-intercept

\newline

(D)

y

-intercept

Identify function type: Identify the type of function given by the equation $y=30\left(\frac{9}{10}\right)^x$ . This is an exponential function of the form $y=a(b)^x$ , where $a$ is the initial value and $b$ is the base of the exponential.
Determine y-intercept: Determine the y-intercept of the graph. $\newline$ The y-intercept occurs when $x=0$ . Plugging $x=0$ into the equation, we get $y=30\left(\frac{9}{10}\right)^0 = 30(1) = 30$ . This shows that the y-intercept is $30$ , which is the coefficient of the exponential expression in the equation.
Analyze other options: Analyze the other options to confirm that they are not constants or coefficients in the equation. $\newline$ (A) Slope: The slope is not constant in an exponential function; it changes at every point on the graph. $\newline$ (B) The value $y$ approaches as $x$ decreases: This would be the horizontal asymptote, which is not explicitly given in the equation. $\newline$ (C) $x$ -intercept: The $x$ -intercept is not given by a constant or coefficient in the equation; it would require setting $y$ to $0$ and solving for $x$ , which is not straightforward in this case.
Conclude characteristic in equation: Conclude which characteristic of the graph is displayed as a constant or coefficient in the equation. $\newline$ The $y$ -intercept is the only characteristic given as a constant or coefficient in the equation, which is $30$ .

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