Which is an exponential decay function? f start bracket x end bracket equals three-fourths start bracket seven-fourths end bracket superscript x f start bracket x end bracket equals two-third start bracket four-fifths end bracket superscript negative x f start bracket x end bracket equals three-halves start bracket eight-sevenths end bracket superscript negative x f start bracket x end bracket equals one-third start bracket negative nine-halves end bracket superscript x

The exponential decay function is ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the exponential decay function

- The general form of an exponential Function is ,

 where a is the initial value and b is growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- The function can be written as

# Remember: if 0 < b < 1 , then 1/b > 1 , then change the negative

  sign of the power by reciprocal the growth factor to decide the

  function is growth or decay

* Lets solve the problem

1.

∵ b = 7/4

∵ 7/4 is greater than 1

∴ f(x) is an exponential growth function

2.

- Change the (-x) to x by reciprocal (4/5) to (5/4)

∴

∵ b = 5/4

∵ 5/4 is greater than 1

∴ f(x) is an exponential growth function

3.

- Change the (-x) to x by reciprocal (8/7) to (7/8)

∴

∵ b = 7/8

∵ 7/8 is greater than 0 and smaller than 1 ⇒ 0 < 7/8 < 1

∴ f(x) is an exponential decay function

* The exponential decay function is

ddsf

step-by-step explanation:

dfs

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.