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

Question

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

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Cherry 6 months 2021-08-09T14:31:36+00:00 1 Answers 3 views 0

Answers ( )

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    2021-08-09T14:33:09+00:00

    Answer:

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

    Step-by-step 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(\frac{5}{4} \right)^{x} is the only one that is increasing in value, as notice that |r| = \frac{5}{4}> 1. Therefore, the correct answer is B.

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