Answer:
The correct answer is [tex]b(x) = 215\cdot \left(\frac{5}{4} \right)^{x}[/tex].
Step-by-step explanation:
We must remember that each option represents a geometrical progression, whose model is represented by:
[tex]y = a\cdot r^{x}[/tex]
Where:
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]a[/tex] - Initial value, dimensionless.
[tex]r[/tex] - Common ration, dimensionless.
A geometric function is decreasing and monotone when [tex]|r| < 1[/tex], stable when [tex]|r| = 1[/tex] and increasing and divergent when [tex]|r| > 1[/tex].
The equation [tex]b(x) = 215\cdot \left(\frac{5}{4} \right)^{x}[/tex] is the only one that is increasing in value, as notice that [tex]|r| = \frac{5}{4}> 1[/tex]. Therefore, the correct answer is B.
