Question

Which equation represents exponential decay?

(1 point)
Responses

f(x)=8x

f x = 8 x

f(x)=0.08x

f x = 0 . 08 x

f(x)=0.2(4)x

f x = 0 . 2 4 x

f(x)=5(2)x

Answer 1

To identify an equation that represents exponential decay, we need to look for a function of the form \( f(x) = a \cdot b^x \) where \( 0 < b < 1 \).

Now, let's analyze the given options:

1. \( f(x) = 8x \) → This is a linear function, not exponential decay.
2. \( f(x) = 0.08x \) → This is also a linear function, not exponential decay.
3. \( f(x) = 0.2(4^x) \) → This represents exponential growth (since \( 4 > 1 \)).
4. \( f(x) = 5(2^x) \) → This also represents exponential growth (since \( 2 > 1 \)).

Since none of these options represent exponential decay, it's worth checking if any options can be miswritten.

None of the options provided indicate a decay scenario. In general, for exponential decay, we would expect a base less than 1.

So, based on the choices you’ve provided, none correctly represents exponential decay. If there are any further details or if I missed an option, please let me know.