3 years ago

Plz answer this question step by step.

Mathematics

1 answer:

pychu [463]3 years ago

8 0

I cant see the picture it is blurry

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Pablo generates the function f(x) = 3/2(5/2)^x-1 to determine the xth number in a sequence. Which is an equivalent representatio

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Answer:

The equivalent function is $f(x)=\dfrac{3}{5}\cdot (\dfrac{5}{2})^{x}$

Step-by-step explanation:

Given: $f(x)=\dfrac{3}{2}\cdot (\dfrac{5}{2})^{x-1}$

This function represents xth number of the sequence.

We need to re-write the function which is equivalent to given one.

First we distribute the exponent x-1

$f(x)=\dfrac{3}{2}\cdot (\dfrac{5}{2})^{x}\cdot (\dfrac{5}{2})^{-1}$ $\because a^{m+n}=a^m\cdot a^n$

$f(x)=\dfrac{3}{2}\cdot (\dfrac{5}{2})^{x}\cdot \dfrac{2}{5}$ $\because (\dfrac{a}{b})^{-1}=\dfrac{b}{a}$

$f(x)=\dfrac{3}{2}\cdot \dfrac{2}{5}\cdot (\dfrac{5}{2})^{x}$

$f(x)=\dfrac{3}{5}\cdot (\dfrac{5}{2})^{x}$

Hence, The equivalent function is $f(x)=\dfrac{3}{5}\cdot (\dfrac{5}{2})^{x}$

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