Which is an exponential decay function?

f(x) = ()x

f(x) = ()–x
f(x) = ()–x
f(x) = ()x

Step-by-step explanation:

Let us understand the exponential function. Here the exponential function is given as under.

Now this is an ever growing exponential function. It never decays unless we have

i) a<1

Hence in this case the function will decays

example

or

ii) x is a negative power.

Example

Now in our problem , the second and third options are same. Hence both can be true. So our answer is b

b)

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752