Exponential growth and decay

The world’s population increases exponentially by 1.1% each year.

Feb/March 2017

Newton’s population is 23 000, and it falls exponentially by 1.4% each year.

Feb/March 2018

A town’s population falls exponentially by 1.7% each year. The current population is 250000.

Feb/March 2020

The number of butterflies in one variety is falling exponentially by $34\%$ each year. By the end of 2014, the population had reached $125.9$ million.

Feb/March 2021

Janna and Kamal each put in $8000. At the end of 12 years, both amounts are $12\,800.

Feb/March 2024

Midhil puts $\$1500$ into an account earning $4.2\%$ compound interest each year. Determine the value of the investment after $5$ years.

Feb/March 2025

Georg puts $5000 into an investment for 14 years at 2% compound interest per year.

May/June 2015

Show that Eduardo has $\$721$ at the end of 6 years, correct to the nearest dollar.

May/June 2015

The world’s population is estimated to be increasing by $1.14\%$ each year. On January $1$st $2014$, the population stood at $7.23$ billion.

May/June 2016

There are 20 000 bacteria at the beginning of the experiment. Their number rises by 30% each hour.

May/June 2016

Marcel puts $2500 into an investment for 3 years at 1.6% per year simple interest. Jacques puts $2000 into an investment for 3 years at $x\%$ per year compound interest. After the 3 years, Marcel and Jacques get the same amount of interest.

May/June 2017

Calculate the percentage decrease in the price.

May/June 2018

A book's price rises from $\$2.50$ to $\$2.65$. Calculate the percentage increase.

May/June 2019

A company’s profit falls exponentially by 0.9% each year. The profit in 2014 was $9500.

May/June 2021

The table gives several values for $y = 2 \times 0.5^x - 1$.

May/June 2021

Carlos puts $4540$ into an account that pays compound interest at $r\%$ per year. By the end of $10$ years, the interest accumulated is $1328.54$.

May/June 2022

Calculate the total number of strawberries altogether.

May/June 2022

Calculate how many trees are in the forest now. Give your answer to the nearest integer.

May/June 2023

Find how many dollars Anil gets.

May/June 2023

Amir places $1500$ into an account. The account earns compound interest at a rate of $r\%$ per year. After 8 years, the investment is worth $1656.73$.

May/June 2024

A car is worth $8000$. After each year, its value falls exponentially by 25%.

May/June 2024

(a) In 2023, a football club recorded 50 adult members and 70 child members. An adult membership fee was $40, whereas a child membership fee was $15.

May/June 2024

Mateo places $1250$ into an investment earning compound interest at a rate of $r\%$ per year. After 6 years, the investment has a total value of $1484$.

May/June 2025

Jess puts $1400 into an account. The account earns compound interest at $r\%$ per year. After 4 years, the investment is worth $1523.15$.

May/June 2025

Hazel puts $1800$ into an account for $7$ years, earning compound interest at $1.5\%$ each year.

Oct/Nov 2015

Calculate the value of the car after 7 years.

Oct/Nov 2015

Find how much the biscuits cost.

Oct/Nov 2015

Split $105$ in the ratio $4 : 3$.

Oct/Nov 2016

Calculate Alberto’s car value after 3 years.

Oct/Nov 2016

A motorbike is priced at $12\,400$. Its value falls exponentially by 15% each year.

Oct/Nov 2017

Adilla puts in $1200 at a compound interest rate of 2.6% per year.

Oct/Nov 2017

As soon as Heidi was born, her grandfather placed some money into an account that paid compound interest. The graph illustrates the exponential increase of this investment.

Oct/Nov 2018

Africa has $30000$ lions. The lion population in Africa falls exponentially by $2\%$ per year.

Oct/Nov 2018

There are 240 students at a school. The ratio girls : boys is 25 : 23.

Oct/Nov 2018

Dina puts $\$600$ into an investment for 5 years at compound interest of $2\%$ per year. Calculate the value of this investment at the end of the 5 years.

Oct/Nov 2019

A town begins with a population of 45 000. That population grows exponentially by 1.6% each year.

Oct/Nov 2020

Calculate the value of this investment at the end of 5 years.

Oct/Nov 2020

Show that Malena has 200 apple trees in all.

Oct/Nov 2021

Calculate the total interest gained after 7 years if simple interest is used.

Oct/Nov 2021

Find the interest gained on the investment after 3 years.

Oct/Nov 2022

Calculate the value of Zak’s investment after 5 years.

Oct/Nov 2022

By the close of 2021, there were $27\,000$ rhinos living in the wild. The rhino population is predicted to fall exponentially by $3\%$ each year.

Oct/Nov 2023

Calculate the car’s value after 1 year.

Oct/Nov 2023

The function is given by $g(x)=4^{x+3}$.

Oct/Nov 2024

At the beginning of the experiment, there are $40\,000$ bacteria. The bacteria population rises by $15\%$ each hour.

Oct/Nov 2024

Find the value for $r$.

Oct/Nov 2024

The mass of a radioactive substance decreases exponentially by 10% each day. Its starting mass is 20 g.

Oct/Nov 2025

Alex invests $200 in an account that pays compound interest at r% each year. By the end of 25 years, the investment is valued at $301.10.

Oct/Nov 2025

Calculate the value of his investment after 4 years.

Oct/Nov 2025

The point (5, 1024) is on the curve $y=c^x$, with c being a whole number.

Oct/Nov 2025

A town has a population of 54 000. This population is falling exponentially by 2% each year.

Oct/Nov 2025