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goldfiish [28.3K]
3 years ago
6

To determine the order that cars line up for the Daytona 500, drivers must complete qualifying laps around the Daytona Internati

onal Speedway. The fastest ever qualifying lap was in 1987 by Bill Elliott, with a time of 42.782 seconds.That was 210.364 miles per hour (or 338.548 kilometers per hour).
A. What was the frequency of the car (measured in laps per second?)

B. How many laps were completed in 60 seconds (1 minute)?
Mathematics
1 answer:
sergey [27]3 years ago
5 0

Answer:

The frequency of the car is 0.0233743 laps/sec and 1.4024 laps were completed in 60 seconds

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Digiron [165]

Answer: 1211.6585 years

<u>Step-by-step explanation:</u>

The equation for exponential growth is: P=P_oe^{kt}

  • P: final population
  • P₀: initial population
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Use the half life information to find k:

\dfrac{1}{2}P_o=P_oe^{k(800)}\\\\\\\dfrac{1}{2}=e^{800k}\qquad \rightarrow \qquad \text{divided both sides by}\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=800k\qquad \rightarrow \qquad \text{applied ln to both sides}\\\\\\\dfrac{ln(\frac{1}{2})}{800}=k\qquad \rightarrow \qquad \text{divided both sides by 800}\\\\\\\large\boxed{-0.000867=k}

Next, input the information (65% decayed = 35% remaining) and the k-value to find your answer.

.35P_o=P_oe^{-0.000867t}\\\\\\.35=e^{-0.000867t}\\\\\\ln(.35)=-0.000867t\\\\\\\dfrac{ln(.35)}{-0.000867}=t\\\\\\\large\boxed{1211.6585=t}

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