Question

question: 1
tik tok analyzes the trend of a new viral dance over time; it was found to follow a quadratic model before dropping off to zero remakes at the end of the dances lifetime. the new dance is released with remakes modeled by the equation $r = -(t - 7)^2 + 64$, where r represents the remakes in thousands and t represents the number of months the dance was viral. according to the equation, what will be the lifetime of dance?

a. 15 years

b. 15 months

c. 15 thousand remakes

d. 7 months

e. 64 months

Explanation:

Step1: Set R to 0 (end of lifetime)

We know that at the end of the dance's lifetime, the number of remakes \( R = 0 \). So we set up the equation \( 0=-(t - 7)^{2}+64 \).

Step2: Solve for t

First, rewrite the equation as \( (t - 7)^{2}=64 \). Taking the square root of both sides, we get \( t - 7=\pm8 \).

• For the positive case: \( t - 7 = 8 \), so \( t=8 + 7=15 \).
• For the negative case: \( t - 7=-8 \), so \( t=-8 + 7=-1 \). Since time cannot be negative, we discard \( t = - 1 \).

Answer:

B. 15 months