Question

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

Answer 1

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.

Answer 2

Decay

Explanation:

Given function,

`y=2(4)^(-x)`

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

`\implies y=2((1)/(4))^x`

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

(i) Growth function : if b > 1

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

Since,
`(1)/(4)` < 1

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