Which equations represent exponential growth? which equations represent exponential decay?

Exponential growth:

2.

3.  

5.

Exponential decay:

1.

4.  

6.  

Step-by-step explanation:

Since we know that an exponential function is in form where a is initial value of function, b is exponential growth or decay. For exponential growth b should be greater than 1 and for exponential decay b should be less than 1

= Exponential growth.

= Exponential decay.

Now let us look at our given equations one by one to determine which one is for exponential growth and which one is for exponential decay.

1.  

In this option a equals 18000 and b equals to 0.78. 0.78 is less than 1, therefore, this equation is representing exponential decay.

2.

We can see that a equals 4,500 and b equals 1.04 and 1.04 is clearly greater than 1 , therefore, this equation is representing exponential growth.

3.  

We can see that a equals 7000 and b equals 1.0575 and 1.0575 is clearly greater than 1 , therefore, this equation is representing exponential growth.

4.  

We can see that a equals 50 and b equals 1/2 and 1/2 (0.5) is clearly less than 1, therefore, this equation is representing exponential decay.

5.

We can see that a equals 45 and b equals 2 and 2 is clearly greater than 1 , therefore, this equation is representing exponential growth.

6.  

We can see that a equals 9000 and b equals 0.9 and 0.9 is clearly less than 1 , therefore, this equation is representing exponential decay.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6