Growth & decay

The value of a second-hand car decreases by 12.1% per year.

Work out the number of full years until the car loses more than half its value. You must show your working.

Here is a formula for an iterative process.

Work out the values of u₁ and u₃

The population of a country is now 67 200 000 The population is predicted to increase by 1% per year for 6 years and then decrease by 1.2% per year for 2 years.

Work out the predicted population of the country 8 years from now. Give your answer to 3 significant figures.

House prices on a street increase by 5.1% each year.

Show that after 14 years the house prices on the street will be at least double.

Rick borrows £1500 from a bank. He pays back £100 each month.

This iterative formula works out the amount he still owes at the end of each month.

Work out the amount he still owes at the end of the 2nd month.

Magana decides to put £500 into an account that pays compound interest. She wants to have at least £560 in the account after 3 years. Work out to 1 decimal place the minimum annual interest rate she needs.

The number of hedgehogs in England is expected to reduce by 4% each year. Assume there are now 1 000 000 hedgehogs in England. Work out the expected number of hedgehogs in England after five years. You must show your working.

The number of hedgehogs in England is expected to reduce by 4% each year. Assume there are now 1 000 000 hedgehogs in England. Work out the expected number of hedgehogs in England after five years. You must show your working.

A sequence of numbers is formed by the iterative process

Circle your answer.

On the same day, Kate buys a car for £14 000 and a painting for £5000

The value of the car decreases by 35% in the first year, and then by 10% each year. The value of the painting increases by 4% each year.

Show that the painting becomes worth more than the car during the fifth year.

£2448 is invested in an account at a rate of compound interest. One year after the investment there is £2496.96 in the account. How much is in the account four years after the investment?

The population of butterflies in a park is 4200

Assume that the population increases by 12% each day. Show that after 20 days the population would be greater than 40 000

In fact, the population increases by 13% each day for 19 days then decreases by 8% for 1 day. After the 20 days, is the actual population greater than 40 000 ?

Show working to support your answer.

The expected number of visitors to the park each day depends on the temperature.

On each of the 30 days in June the park is open the probability that the temperature is less than 21°C is 0.4 Work out the total number of expected visitors to the park in June.

A sequence of numbers is formed by the iterative process

Work out the values of u₂ and u₃

u 2 =

A marathon takes place each year. In 2020 there were 6500 runners.

Prediction For each of the next 3 years the number of runners will increase by 5%

Does this predict that in 2023 there will be more than 7500 runners? You must show your working.

The value of a house is £120 000 The value is expected to increase by 5% each year. Work out the expected value after 4 years. Give your answer to 2 significant figures. You must show your working.

The value of a house is £120 000 The value is expected to increase by 5% each year. Work out the expected value after 4 years. Give your answer to 2 significant figures. You must show your working.

Mia wants to borrow £6000 and repay it, with interest, after two years. She sees two offers for loans.

Mia says, “I will pay back the same amount because the average of 1% and 5% is 3%”

Is she correct? You must show your working.

Mia wants to borrow £6000 and repay it, with interest, after two years. She sees two offers for loans.

Mia says, “I will pay back the same amount because the average of 1% and 5% is 3%” Is she correct? You must show your working.

Doug owes an amount of £600 He wants to pay back this amount in five months. He says, “Each month, I will pay back 20% of the amount I still owe.” Show working to check if his method is correct.

Doug owes an amount of £600 He wants to pay off this amount in five months. He says, “Each month, I will pay back 20% of the amount I still owe.” Show working to check if his method is correct.

Investment A Save £150 per month for 2 years. 2.5% interest is added to the total amount saved. Investment B Invest £3500 Compound interest is added at 3% per year. After 2 years, how much more is investment B worth than investment A?

A sequence of numbers is formed by the iterative process

Work out the values of u₂ and u₃

Mirek invests £6000 at a compound interest rate of 1.5% per year. He wants to earn more than £1000 interest. Work out the least time, in whole years, that this will take.

The value of a new car is £18 000 The value of the car decreases by 25% in the first year 12% in each of the next 4 years. Work out the value of the car after 5 years.