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Worksheet: Exponential Population Growth

Q1:

An apple loses 50% of its water content after 30 days due to dehydration. If an apple weighed 100 g when it was picked, and 84 g10 days later, after roughly how many days will the apple weigh 50 g?

  • A 55 days
  • B 35 days
  • C 42 days
  • D 45 days
  • E 40 days

Q2:

We consider that computers lose 2 5 % of their value every year.

Write a corresponding formula for the value 𝑉 of a computer 𝑦 years after its purchase. Let 𝑉 0 be its purchase value.

  • A 𝑉 = 𝑉 0 𝑦
  • B 𝑉 = 𝑉 β‹… 0 . 2 5 0 𝑦
  • C 𝑉 = 𝑉 β‹… 1 . 2 5 0 𝑦
  • D 𝑉 = 𝑉 β‹… 0 . 7 5 0 𝑦
  • E 𝑉 = 𝑉 β‹… 1 . 7 5 0 𝑦

Rewrite the expression for the value 𝑉 of a computer 𝑦 years after its purchase in the form 𝑉 = 𝑉 β‹… 𝑏 0 1 2 𝑦 .

  • A 𝑉 = 𝑉 β‹… 0 . 9 7 6 0 1 2 𝑦
  • B 𝑉 = 𝑉 β‹… 0 . 2 5 0 1 2 𝑦
  • C 𝑉 = 𝑉 β‹… 0 . 7 5 0 1 2 𝑦
  • D 𝑉 = 𝑉 β‹… 0 . 0 2 4 0 1 2 𝑦
  • E 𝑉 = 𝑉 β‹… 0 . 0 3 1 6 7 0 1 2 𝑦

Deduce from your previous answer the percentage of the monthly depreciation of computers.

Q3:

The number of Ebola infections in West Africa at the start of an epidemic followed an exponential growth. It is given by 𝑁 = 𝑒 0 . 0 7 5 𝑑 , with 𝑑 the number of days after the first infection.

What does the coefficient 0.075 represent?

  • AIt is the time it takes for the number of infections to be multiplied by 𝑒 .
  • BIt is the number of new infections per day.
  • CIt is the percentage of the daily growth in the number of infections ( 7 . 5 % ).
  • D 1 0 . 0 7 5 is the time it takes for the number of infections to be multiplied by 𝑒 .
  • EIt is the number of days after the first infection.

By rewriting the formula in the form 𝑁 = 𝑏 𝑑 , find the percentage of the daily growth in the number of infections. Give your answer to one decimal place.

  • A 7 . 8 %
  • B 7 7 . 8 %
  • C 1 7 . 8 %
  • D 7 . 5 %
  • E 9 2 . 2 %

Q4:

Moore’s law was named after Gordon Moore who observed in the sixties that, owing to miniaturization, the number of transistors in a dense integrated circuit doubles approximately every two years. He predicted that this will last for at least one decade.

Using Moore’s law, find an explicit formula for the number of transistors in a single circuit in a year 𝑦 . Assume that in 1971, a circuit had 2 3 0 0 transistors.

  • A 𝑁 = 2 3 0 0 β‹… 2 2 ( 𝑦 βˆ’ 1 9 7 1 )
  • B 𝑁 = 2 3 0 0 β‹… 2 𝑦 βˆ’ 1 9 7 1
  • C 𝑁 = 2 3 0 0 β‹… 2 𝑦 2
  • D 𝑁 = 2 3 0 0 β‹… 2 𝑦 βˆ’ 1 9 7 1 2
  • E 𝑁 = 2 𝑦 βˆ’ 1 9 7 1 2

In 2011, 2.6 billion transistors were used to make a single integrated circuit (a 10-core Xeon Westmere-EX processor). Would you consider that Moore’s law was still valid in 2011?

  • Ayes
  • Bno

In 2017, 9.7 billion transistors were used to make a single integrated circuit at IBM and 19.2 billion transistors for a 32-core AMD Epyc processor. Which of these figures can be considered to fit with Moore’s law?

Q5:

The temperature decreases by 1 ∘ C every 2 hours from 6 pm to 5 am. Can this be represented by a linear or an exponential decay model?

  • Aa linear decay model
  • Ban exponential decay model