Question

Which function has the slowest rate of growth as x approaches infinity?(1 point)
Responses

y=5x2
y is equal to 5 x squared

y=−3x2
y is equal to negative 3 x squared

y=5(1.2)x
y is equal to 5 times 1 point 2 to the x th power

y=4(0.8)x

Answer 1

To determine which function has the slowest rate of growth as \( x \) approaches infinity, we can analyze the functions given:

1. \( y = 5x^2 \)
2. \( y = -3x^2 \) (growth behavior is determined by the term \( x^2 \) since it's dominated by negative growth)
3. \( y = 5(1.2)^x \)
4. \( y = 4(0.8)^x \)

As \( x \) approaches infinity:

- The quadratic functions (\(y = 5x^2\) and \(y = -3x^2\)) both grow without bound in magnitude. However, \( y = -3x^2 \) goes to \( -\infty \), which is not a "growth" in the positive sense but indicates it decreases.

- The function \( y = 5(1.2)^x \) is an exponential function, which grows exponentially as \( x \) increases.

- The function \( y = 4(0.8)^x \) is also an exponential function but since \( 0.8 < 1 \), it decays towards \( 0 \) as \( x \) approaches infinity.

Among the options, \( y = 4(0.8)^x \) has the slowest growth since it approaches \( 0 \) as \( x \) approaches infinity, while the other functions either grow positively or negatively without bound.

Thus, the function with the slowest rate of growth as \( x \) approaches infinity is:

**\( y = 4(0.8)^x \)**.