Which equations represent exponential growth?Which equations represent exponential decay?Drag the choices into the boxes to complete the table.
Accepted Solution
A:
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.