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In this lesson, we will learn how to describe and solve real-world problems that include exponential growth or decay.
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
10 days later it weighed
after roughly how many days
will the apple weigh 50 g?
We consider that computers lose
of their value every year.
Write a corresponding formula for the value
of a computer
years after its purchase. Let
be its purchase value.
Rewrite the expression for the value
of a computer
years after its purchase in the form
Deduce from your previous answer the percentage of the monthly depreciation of computers.
The number of Ebola infections in West Africa at the start of
an epidemic followed an exponential growth. It is given by
the number of days after the first infection.
What does the coefficient 0.075 represent?
By rewriting the formula in the form
find the percentage of the daily growth in the number of infections. Give your answer to one decimal place.
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
. Assume that in 1971, a circuit had
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?
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?
The temperature decreases by
2 hours from 6 pm to 5 am. Can this be represented by a linear or an exponential decay model?
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