Which of the following statements about the graph of y=12(0.75)^(x) is true? Choose 1 answer: A As x increases, y increases at an increasing rate. (B) As x increases, y increases at a decreasing rate. (C) As x increases, y decreases at an increasing rate. (D) As x increases, y decreases at a decreasing rate.

Analyze Function: We need to analyze the function y=12(0.75)^(x) to determine how y changes as x increases. The base of the exponent, 0.75, is less than 1, which typically indicates an exponential decay.Exponential Decay: Since the base 0.75 is between 0 and 1, as x increases, the value of (0.75)^(x) decreases. This is because any number less than 1 raised to a higher power gets smaller.Positive Coefficient: The coefficient 12 is a positive constant multiplier. This means that as (0.75)^(x) gets smaller, the entire expression 12(0.75)^(x) also gets smaller, but it remains positive because 12 is positive.Rate of Change: Now we need to determine the rate of change of y as x increases. Since 0.75 is a constant factor less than 1, each time x increases by 1, y is multiplied by 0.75, which means y decreases. However, the amount by which y decreases gets smaller each time because the remaining y value is smaller. This is a decreasing rate.Conclusion: Based on the analysis, we can conclude that as x increases, y decreases, and it does so at a decreasing rate. This matches option (D) from the given choices.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following statements about the graph of
y=12(0.75)^(x) is true?
Choose 1 answer:
A As
x increases,
y increases at an increasing rate.
(B) As
x increases,
y increases at a decreasing rate.
(C) As
x increases,
y decreases at an increasing rate.
(D) As
x increases,
y decreases at a decreasing rate.

Which of the following statements about the graph of $y=12(0.75)^{x}$ is true? $\newline$ Choose $1$ answer: $\newline$ A As $x$ increases, $y$ increases at an increasing rate. $\newline$ (B) As $x$ increases, $y$ increases at a decreasing rate. $\newline$ (C) As $x$ increases, $y$ decreases at an increasing rate. $\newline$ (D) As $x$ increases, $y$ decreases at a decreasing rate.

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of equations using any method: word problems

Full solution

Q. Which of the following statements about the graph of

y=12(0.75)^{x}

is true?

\newline

Choose

1

answer:

\newline

A As

x

increases,

y

increases at an increasing rate.

\newline

(B) As

x

increases,

y

increases at a decreasing rate.

\newline

x

increases,

y

decreases at an increasing rate.

\newline

(D) As

x

increases,

y

decreases at a decreasing rate.

Analyze Function: We need to analyze the function $y=12(0.75)^{x}$ to determine how $y$ changes as $x$ increases. The base of the exponent, $0.75$ , is less than $1$ , which typically indicates an exponential decay.
Exponential Decay: Since the base $0.75$ is between $0$ and $1$ , as $x$ increases, the value of $(0.75)^{x}$ decreases. This is because any number less than $1$ raised to a higher power gets smaller.
Positive Coefficient: The coefficient $12$ is a positive constant multiplier. This means that as $(0.75)^{x}$ gets smaller, the entire expression $12(0.75)^{x}$ also gets smaller, but it remains positive because $12$ is positive.
Rate of Change: Now we need to determine the rate of change of $y$ as $x$ increases. Since $0.75$ is a constant factor less than $1$ , each time $x$ increases by $1$ , $y$ is multiplied by $0.75$ , which means $y$ decreases. However, the amount by which $y$ decreases gets smaller each time because the remaining $y$ value is smaller. This is a decreasing rate.
Conclusion: Based on the analysis, we can conclude that as $x$ increases, $y$ decreases, and it does so at a decreasing rate. This matches option $(D)$ from the given choices.