Answer:
[tex]f(5)=125[/tex]
Step-by-step explanation:
If [tex]f(1)=3.2[/tex] and [tex]f(x+1)=\dfrac{5}{2}f(x),[/tex] then
- at [tex]x=1[/tex] you have [tex]f(2)=\dfrac{5}{2}\cdot f(1)=2.5\cdot 3.2=8;[/tex]
- at [tex]x=2[/tex] you have [tex]f(3)=\dfrac{5}{2}\cdot f(2)=2.5\cdot 8=20;[/tex]
- at [tex]x=3[/tex] you have [tex]f(4)=\dfrac{5}{2}\cdot f(3)=2.5\cdot 20=50;[/tex]
- at [tex]x=4[/tex] you have [tex]f(5)=\dfrac{5}{2}\cdot f(4)=2.5\cdot 50=125.[/tex]
