Question 5 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY
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?
Answer
A
f of x is equal to 48 times 3 fourths raised to the x minus 1 power
B
f of x is equal to 48 times 5 sixths raised to the x minus 1 power
C
f of x is equal to 64 times 3 fourths raised to the x minus 1 power
D
f of x is equal to 64 times 5 sixths raised to the x minus 1 power
Explanation
The first height is 64 inches, so the first term is 64. The common ratio is 48 ÷ 64 = 3/4; checking the next peak gives 36 ÷ 48 = 3/4 as well. Thus the explicit rule is f(x) = 64(3/4)^(x − 1), which is choice B.
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