Answered

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A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. Which explicit function represents the geometric sequence of the heights of the toy?
a. F(x)=48( 5/6 )ˣ⁻¹
b. F(x)=48( 3/4 )ˣ⁻¹
c. F(x)=64( 3/4 )ˣ⁻¹
d. F(x)=64( 5/6 )ˣ⁻¹

Sagot :

sqdancefan

Answer:

  c. F(x)=64( 3/4 )ˣ⁻¹

Step-by-step explanation:

You want the explicit function that describes the sequence 64, 48, 36, ....

Initial value

The first number in the sequence is F(1) = 64. (This eliminates choices A and B.)

Ratio

The common ratio of numbers in the sequence is ...

  [tex]r=\dfrac{48}{64}=\dfrac{36}{48}=\dfrac{3}{4}\qquad\text{eliminates choice D}[/tex]

Function

The explicit function can be written as ...

  [tex]F(x)=F(1)\cdot r^{x-1}\\\\\boxed{F(x)=64\left(\dfrac{3}{4}\right)^{x-1}}\qquad\text{matches choice C}[/tex]

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