Mathematics

Problem

Consider the function

p(x)=4\,(0.8)^{x}

. Which of the following statements correctly describes its graph? a) It is an increasing curve with y-intercept

4

and horizontal asymptote

y=0

. b) It is a decreasing curve with y-intercept

4

and horizontal asymptote

y=0

. c) It is a decreasing curve with y-intercept

0.8

and horizontal asymptote

y=0

. d) It is a decreasing curve with y-intercept

0.8

and horizontal asymptote

y=4

Intuitive explanation

This is an exponential decay problem—you're identifying how a function behaves when its base is between 0 and 1. The key insight is that the base $0.8$ is a fraction less than 1, which means each time $x$ increases by 1, the output shrinks by 20%. Look for a statement describing a decreasing curve that approaches zero as $x$ grows, starts at $y = 4$ when $x = 0$ , and never goes negative.

Intuitive explanation

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