A function [tex]f(x)=b\cdot a^x[/tex] shows
- exponential growth, if [tex]a>1;[/tex]
- exponential decay, if [tex]0<a<1.[/tex]
Consider all options:
A. The function [tex]f(x)=0.4\cdot 3^x[/tex] shows exponential growth, because [tex]3>1.[/tex]
B. The function [tex]f(x)=3\cdot 0.5^x[/tex] shows exponential decay, because [tex]0<0.5<1.[/tex]
C. The function [tex]f(x)=0.8\cdot 0.9^x[/tex] shows exponential decay, because [tex]0<0.9<1.[/tex]
D. The function [tex]f(x)=0.9\cdot 5^{-x}=0.9\cdot \left(\dfrac{1}{5}\right)^x[/tex] shows exponential decay, because [tex]0<\dfrac{1}{5}<1.[/tex]
Answer: correct choice is A
