Answer:
5
Explanation:
The function is [tex]f(x) = 2 \cdot 5^{x}[/tex], which means that an increase of a unit in x leads to a multiplicative rate of change of 5 in y. For instance:
[tex]f(1) = 2\cdot 5^{1}[/tex]
[tex]f(1) = 10[/tex]
[tex]f(2) = 2 \cdot 5^{2}[/tex]
[tex]f(2) = 2 \cdot 5\cdot 5[/tex]
[tex]f(2) = 50[/tex]
[tex]f(2) = f(1) \cdot 5[/tex]
[tex]f(3) = 2\cdot 5^{3}[/tex]
[tex]f(3) = 2 \cdot 5\cdot 5 \cdot 5[/tex]
[tex]f(3) = f(2) \cdot 5[/tex]
Therefore, it is proven that:
[tex]f(n) = 5 \cdot f(n-1)[/tex]
