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Each of the functions below model the monetary value of an item. Which is the only

that has a growth factor showing the item is increasing in value?

O a(x) = 90(3/4)^x

B(x) = 215(5/4)^x

c(x) = 73(0.98)^x

d(x) = 12(0.24)^x

User StephQ
by
7.6k points

1 Answer

4 votes

Answer:

The correct answer is
b(x) = 215\cdot \left((5)/(4) \right)^(x).

Explanation:

We must remember that each option represents a geometrical progression, whose model is represented by:


y = a\cdot r^(x)

Where:


y - Dependent variable, dimensionless.


a - Initial value, dimensionless.


r - Common ration, dimensionless.

A geometric function is decreasing and monotone when
|r| < 1, stable when
|r| = 1 and increasing and divergent when
|r| > 1.

The equation
b(x) = 215\cdot \left((5)/(4) \right)^(x) is the only one that is increasing in value, as notice that
|r| = (5)/(4)> 1. Therefore, the correct answer is B.

User Anand Mahajan
by
8.7k points

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