Question

MEDAL FOR ANSWER PLEASE HELP





Select all of the equations that will produce exponential decay. (More than one can be chosen)






1: y=(0.1)^x
2: y=2(1/4)^x
3: y=(3)^x
4: y=1/2 (5)^x
5: y=(2)^x
6: y = 3(0.4)^x

Answer 1

In an equation of the form:

\(y = ak^x\)

where a is a positive number, you will have exponential decay if \(0 \le k \lt 1\)

Answer 2

I don't get it

Answer 3

If you raise a number larger than 1 to larger and larger exponents starting with 1, the number gets larger and larger.
For example,
2^1 = 2
2^2 = 4
2^3 = 8
By raising 2 to a larger and larger exponent, the result is a larger number.

Now try raising a number between 0 and 1 to larger and larger exponents.
For example, raise 1/10 to larger and larger powers.
(1/10)^1 = 1/10
(1/10)^2 = 1/100
(1/10^3 = 1/1000
As you can see, the numbers get smaller and smaller.

Answer 4

Exponential decay is based on a number between 0 and 1 being raised to a larger and larger power and giving you smaller results.

Answer 5

so i need to answer all the choices and every one that is smaller is right?

Answer 6

Look at all the functions in your choices.
They all have x as an exponent.
As x becomes larger and larger, if what is being raised to x is between 0 and 1, the result will get smaller and smaller.

Answer 7

All the choices that have a number between 0 and 1 being raised to x are exponential decay.
If the number being raised to x is larger than 1, then it is exponential growth.

Answer 8

so if x is 0 1 or in between its decay right?

Answer 9

1: y=(0.1)^x <--- 0.1 is being raised to x
2: y=2(1/4)^x <--- 1/4 is being raised to x
3: y=(3)^x <--- 3 is being raised to x
4: y=1/2 (5)^x <--- etc.
5: y=(2)^x
6: y = 3(0.4)^x

Answer 10

I think you're on the right track, but it's not exactly as you stated.
1. It's a number being raised to x, not x being raised to a power.
2. The number being raised to x cannot be 0 or 1. It must be in between 0 and 1 for decay.

Answer 11

I started going through the choices above.
Do you see what I did?
Choices 1 and 2 have 1/10 and 1/4 raised to x.
Since 1/10 and 1/4 are both between 0 and 1, choices 1 and 2 are exponential decay.
Now look at choice 3. The number being raised to x is 3. 3 is not between 0 and 1, so choice 3 is not exponential decay.

Answer 12

Now look at choices 4, 5, and 6.
Which ones have a number between 0 and 1 being raised to x?
The ones that do are exponential decay.

Answer 13

are the ones in parenthesis being raised to x?

Answer 14

because if they are the only other one i would think that is decay is 6

Answer 15

Thank you @mathstudent55

Answer 16

Correct.
Choices 1, 2, and 6 are decay.

Answer 17

You're welcome.