Question

Which function represents exponential decay? f(x) = One-half(2)x f(x) = Three-fourths(Negative one-fifth)x f(x) = 3(Seven-halves)x f(x) = 2(Two-thirds)x

Answer 1

Answer:              $f(x)=2(\dfrac{2}{3})^x$

Step-by-step explanation:

We know that the exponential decay equation is given by :-

$y=Ab^x$

, where A = initial value.

b = Multiplicative growth rate  ( b <1 for decay)

x= time period.

Note : b ≠1 and b>0.

Let's check all the functions:

• $f(x)=\dfrac{1}{2}(2)^x$

, here b =2 >1 , so this function does not represent exponential decay.

• $f(x)=\dfrac{3}{4}(-\dfrac{1}{5})$

here b = $-\dfrac{1}{5}$  but b should be greater than 0 for exponential function, so this function does not represent exponential decay.

• $f(x)=3(\dfrac{7}{2})^x$

Here , $b=\frac{7}{2}>1$ , so this function does not represent exponential decay.

• $f(x)=2(\dfrac{2}{3})^x$

Here , $b=\dfrac{2}{3}$  , so this function represents exponential decay.

Hence, the correct answer is $f(x)=2(\dfrac{2}{3})^x$ .

Answer 2

Answer:

D on edg

Step-by-step explanation: