# Worksheet: Exponential Population Growth

In this worksheet, we will practice describing and solving real-world problems that include exponential growth or decay.

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 10 days later it weighed 80 g, 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 of their value every year.

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

• A
• B
• C
• D
• E

Rewrite the expression for the value of a computer years after its purchase in the form .

• A
• B
• C
• D
• E

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

Q3:

Mooreβ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 Mooreβ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 transistors.

• A
• B
• C
• D
• E

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 Mooreβ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 Mooreβs law?

Q4:

The number of Ebola infections in West Africa at the start of an epidemic followed an exponential growth. It is given by , with 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 .
• BIt is the number of new infections per day.
• CIt is the percentage of the daily growth in the number of infections ().
• D is the time it takes for the number of infections to be multiplied by .
• EIt is the number of days after the first infection.

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.

• A
• B
• C
• D
• E

Q5:

The temperature decreases by 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