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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Exponential growth and decay

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:exponential_growth_and_decay/5309/


Example 1.

The research organization in England conducted a telephone survey on the role of bicycles in the daily lives of respondents. They asked 4 questions and received the following answers from 500 respondents:

  • Do you ride a bike? (N = 500)

    • Yes, often - 20 %

    • Yes, sometimes - 35 %

    • Never - 45 %

  • What kind of rides do you use it for? (Only those who cycle regularly or occasionally answered; N = 275)

    • For sports and recreation - 74.3 %

    • For driving to the store and errands - 35.7 %

    • For driving to work 10 %

    • Other - 4 %

  • How do you get to work or to college? (only employees and students answered; N = 233)

    • On foot - 21 %

    • By a bike - 7 %

    • With public transport - 9 %

    • By a car - 63 %

  • Would you be willing to give up your car for a ride to work and ride a bike regularly at least once a week? (Only employees and students driving to work or college were asked; N = 147)

    • Yes - 30 %

    • Yes, I'm already doing it - 5.6 %

    • No - 64.4 %


Find out:

  • What is the population in the survey?

  • Is the sample random?

  • What do you think of its representativeness?

  • Can we, on the basis of this research, declare British a non-cycling nation?

    
Example 2.

300,000 people live in an American city. One color-blind person was listed in a sample of hundred people. How many color-blind (statistically) people are expected to live in the city?