a bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches…

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?\n f(x)=48left(\frac{5}{6}\right)^{x - 1}\n f(x)=48left(\frac{3}{4}\right)^{x - 1}\n f(x)=64left(\frac{3}{4}\right)^{x - 1}\n f(x)=64left(\frac{5}{6}\right)^{x - 1}

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?\n f(x)=48left(\frac{5}{6}\right)^{x - 1}\n f(x)=48left(\frac{3}{4}\right)^{x - 1}\n f(x)=64left(\frac{3}{4}\right)^{x - 1}\n f(x)=64left(\frac{5}{6}\right)^{x - 1}

Answer

Explanation:

Step1: Identify the first - term and common ratio

The first - term $a_1$ of the geometric sequence is the height at the first peak, so $a_1 = 64$. The common ratio $r$ of a geometric sequence is found by dividing a term by its previous term. So $r=\frac{48}{64}=\frac{3}{4}$.

Step2: Recall the formula for the $n$th term of a geometric sequence

The formula for the $n$th term of a geometric sequence is $f(x)=a_1r^{x - 1}$, where $a_1$ is the first - term and $r$ is the common ratio.

Step3: Substitute the values of $a_1$ and $r$ into the formula

Substituting $a_1 = 64$ and $r=\frac{3}{4}$ into the formula $f(x)=a_1r^{x - 1}$, we get $f(x)=64(\frac{3}{4})^{x - 1}$.

Answer:

$f(x)=64(\frac{3}{4})^{x - 1}$