Question

Which equations represent exponential growth?

Answer 1

Answer:

Exponential growth:

2. $P=4500(1.04)^{t}$

3.  $A=7000(1.0575)^{t}$

5. $P=45(2)^{t}$

Exponential decay:

1. $V=18000(0.78)^{t}$

4.  $P=50(\frac{1}{2})^{t}$

6. $A=9000(0.9)^{t}$  

Step-by-step explanation:

Since we know that an exponential function is in form $y=a\cdot b^{x}$ 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

$b>1$ = Exponential growth.

$b$ = 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. $V=18000(0.78)^{t}$  

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. $P=4500(1.04)^{t}$

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.  $A=7000(1.0575)^{t}$

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.  $P=50(\frac{1}{2})^{t}$

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. $P=45(2)^{t}$

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. $A=9000(0.9)^{t}$  

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.