Question

Which is an exponential decay function?

Answer 1

Step-by-step explanation:

exponential decay functions are written in the form :

$y=ab^{x}$

where b is less than 1

if we look at the 3rd choice and consider the term on the right.

$(8/7)^{-x}$

= $(7/8)^{x}$

If we compare this to the general form above,

b = 7/8 (which is less than 1)

hence the 3rd choice is correct.

Answer 2

Answer:

The function which is an exponential decay function is:

                       $f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}$

Step-by-step explanation:

We know that an exponential  function is in the form of:

          $f(x)=ab^x$

where a>0 and  if 0<b<1 then the function is a exponential decay function.

and if b>1 then the function is a exponential growth function.

a)

$f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x$

Here

$b=\dfrac{7}{4}>1$

Hence, the function is a exponential growth function.

b)

$f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}$

We know that:

$a^{-x}=(\dfrac{1}{a})^x$

Hence, we have the function f(x) as:

$f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x$

Here

$b=\dfrac{5}{4}>1$

Hence, the function is a exponential growth function.

c)

$f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}$

We know that:

$a^{-x}=(\dfrac{1}{a})^x$

Hence, we have the function f(x) as:

$f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x$

Here

$b=\dfrac{7}{8}$

Hence, the function is a exponential decay function.

d)

$f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x$

Here

$b=\dfrac{9}{2}>1$

Hence, the function is a exponential growth function.