Question

Does the following equation represent growth or decay? y = 2(4)^-x

Answer 1

Answer:

Decay

Step-by-step explanation:

Given function,

$y=2(4)^{-x}$

$\implies y = 2(4^{-1})^x$   $(\because a^{mn}=(a^m)^n)$

$\implies y=2(\frac{1}{4})^x$

∵ An exponential function $y=ab^x$ is,

(i) Growth function : if b > 1

(ii) Decay function : if 0 < b < 1

Since, $\frac{1}{4}$ < 1

Hence, the exponential function $y=2(4)^{-x}$ is a decay function.

Answer 2

I believe the correct answer from the choices would be the former. The expression y = 2(4)^-x would represent an exponential growth considering there is multiplication involved. Hope this answers the question. Have a nice day. Feel free to ask more questions.