Answer:
Exponential growth functions are:
![A=20000(1.08)^{t}](https://tex.z-dn.net/?f=A%3D20000%281.08%29%5E%7Bt%7D)
![A=40(3)^{t}](https://tex.z-dn.net/?f=A%3D40%283%29%5E%7Bt%7D)
![A=1700(1.07)^{t}](https://tex.z-dn.net/?f=A%3D1700%281.07%29%5E%7Bt%7D)
Exponential decay functions are:
![A=80(\frac{1}{2})^{t}=80(0.5)^{t}](https://tex.z-dn.net/?f=A%3D80%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bt%7D%3D80%280.5%29%5E%7Bt%7D)
![A=1600(0.8)^{t}](https://tex.z-dn.net/?f=A%3D1600%280.8%29%5E%7Bt%7D)
![A=1700(0.93)^{t}](https://tex.z-dn.net/?f=A%3D1700%280.93%29%5E%7Bt%7D)
Step-by-step explanation:
Given:
An exponential function is of the form
, where,
.
Now, if a > 0 and b > 1, then the exponential function represent exponential growth.
If a > 0 and 0 < b < 1, then the exponential function represent exponential decay.
Let us check each function now.
Option 1: ![A=20000(1.08)^{t}](https://tex.z-dn.net/?f=A%3D20000%281.08%29%5E%7Bt%7D)
Here, ![a = 20000, b = 1.08](https://tex.z-dn.net/?f=a%20%3D%2020000%2C%20b%20%3D%201.08)
As 1.08 > 1, the function is exponential growth.
Option 2: ![A=80(\frac{1}{2})^{t}=80(0.5)^{t}](https://tex.z-dn.net/?f=A%3D80%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bt%7D%3D80%280.5%29%5E%7Bt%7D)
Here, ![a = 80, b = 0.50](https://tex.z-dn.net/?f=a%20%3D%2080%2C%20b%20%3D%200.50)
As 0.5 < 1, the function is exponential decay.
Option 3: ![A=1600(0.8)^{t}](https://tex.z-dn.net/?f=A%3D1600%280.8%29%5E%7Bt%7D)
Here, ![a = 1600, b = 0.8](https://tex.z-dn.net/?f=a%20%3D%201600%2C%20b%20%3D%200.8)
As 0.8 < 1, the function is exponential decay.
Option 4: ![A=40(3)^{t}](https://tex.z-dn.net/?f=A%3D40%283%29%5E%7Bt%7D)
Here, ![a = 40, b = 3](https://tex.z-dn.net/?f=a%20%3D%2040%2C%20b%20%3D%203)
As 3 > 1, the function is exponential growth.
Option 5: ![A=1700(1.07)^{t}](https://tex.z-dn.net/?f=A%3D1700%281.07%29%5E%7Bt%7D)
Here, ![a = 1700, b = 1.07](https://tex.z-dn.net/?f=a%20%3D%201700%2C%20b%20%3D%201.07)
As 1.07 > 1, the function is exponential growth.
Option 6: ![A=1700(0.93)^{t}](https://tex.z-dn.net/?f=A%3D1700%280.93%29%5E%7Bt%7D)
Here, ![a = 1700, b = 0.93](https://tex.z-dn.net/?f=a%20%3D%201700%2C%20b%20%3D%200.93)
As 0.93 < 1, the function is exponential decay.