Answer:
Exponential growth:
2. [tex]P=4500(1.04)^{t}[/tex]
3. [tex]A=7000(1.0575)^{t}[/tex]
5. [tex]P=45(2)^{t}[/tex]
Exponential decay:
1. [tex]V=18000(0.78)^{t}[/tex]
4. [tex]P=50(\frac{1}{2})^{t}[/tex]
6. [tex]A=9000(0.9)^{t}[/tex]
Step-by-step explanation:
Since we know that an exponential function is in form [tex]y=a\cdot b^{x}[/tex] 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
[tex]b>1[/tex] = Exponential growth.
[tex]b<1[/tex] = 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. [tex]V=18000(0.78)^{t}[/tex]
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. [tex]P=4500(1.04)^{t}[/tex]
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. [tex]A=7000(1.0575)^{t}[/tex]
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. [tex]P=50(\frac{1}{2})^{t}[/tex]
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. [tex]P=45(2)^{t}[/tex]
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. [tex]A=9000(0.9)^{t}[/tex]
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.
