Question

For which function does f decrease by 15% every time x increase by 1? A: f(x)= 0.15^x B: f(x)=8.5^x C: f(x)=15^x. D: f(x)=85^x

Answer 1

Answer:

$f(x) = (0.85)^x$

Step-by-step explanation:

Exponential amount of decay:

The equation for an amount that decays exponentially has the following format:

$A(x) = A(0)(1 - r)^x$

In which r is the decay rate, as a decimal.

Decrease by 15%

This means that $r = 0.15$. So

$f(x) = (1 - r)^x = (1 - 0.15)^x = (0.85)^x$

So

$f(x) = (0.85)^x$