Answer:
Exponential growth functions are:
[tex]A=20000(1.08)^{t}[/tex]
[tex]A=40(3)^{t}[/tex]
[tex]A=1700(1.07)^{t}[/tex]
Exponential decay functions are:
[tex]A=80(\frac{1}{2})^{t}=80(0.5)^{t}[/tex]
[tex]A=1600(0.8)^{t}[/tex]
[tex]A=1700(0.93)^{t}[/tex]
Step-by-step explanation:
Given:
An exponential function is of the form [tex]y=ab^{x}[/tex], where, [tex]a\ne 0[/tex].
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: [tex]A=20000(1.08)^{t}[/tex]
Here, [tex]a = 20000, b = 1.08[/tex]
As 1.08 > 1, the function is exponential growth.
Option 2: [tex]A=80(\frac{1}{2})^{t}=80(0.5)^{t}[/tex]
Here, [tex]a = 80, b = 0.50[/tex]
As 0.5 < 1, the function is exponential decay.
Option 3: [tex]A=1600(0.8)^{t}[/tex]
Here, [tex]a = 1600, b = 0.8[/tex]
As 0.8 < 1, the function is exponential decay.
Option 4: [tex]A=40(3)^{t}[/tex]
Here, [tex]a = 40, b = 3[/tex]
As 3 > 1, the function is exponential growth.
Option 5: [tex]A=1700(1.07)^{t}[/tex]
Here, [tex]a = 1700, b = 1.07[/tex]
As 1.07 > 1, the function is exponential growth.
Option 6: [tex]A=1700(0.93)^{t}[/tex]
Here, [tex]a = 1700, b = 0.93[/tex]
As 0.93 < 1, the function is exponential decay.
