Growth and Decay Questions

Stephanie is given a 7% pay rise. She is currently earning £24,000 a year. Circle the calculation which works out her new salary.

• 24000 x 0.07

• 24000 x 1.07

• 24000 + 1.07

• 24000 ÷ 1.07

Answer explanation

To calculate Stephanie's new salary after a 7% pay rise, multiply her current salary by 1.07. This accounts for her original salary plus the 7% increase. Therefore, the correct calculation is 24000 x 1.07.

Assuming Stephanie gets the same pay rise every year, circle the calculation which calculates Stephanie’s salary after 5 years of working there.

• 1.07 x 24000⁵

• 24000 x 5¹.⁰⁷

• 24000 x 1.07⁵

• 24000¹.⁰⁷ x 5

Answer explanation

The correct calculation for Stephanie's salary after 5 years is 24000 x 1.07⁵. This formula accounts for a consistent annual pay rise of 7%, compounded over 5 years.

James starts on a salary of £23500. He gets a raise of 6% every year. Write down the calculation James would use to calculate his salary after 9 years.

• £23500 * 0.06 * 9

• £23500 + (23500 * 0.06 * 9)

• £23500 * 9 * 0.06

Answer explanation

James's salary increases by 6% each year, so to find his salary after 9 years, he uses the formula for compound interest: £23500 * (1 + 0.06)^9, which accounts for the annual raises.

A car loses 4% of its value every year. In 2019, the car is worth £12,000. How much will the car be worth in 2024?

• £9,830.48

• £10,000.00

• £9,600.00

• £11,520.00

Answer explanation

The car's value decreases by 4% each year. After 5 years (2019 to 2024), the value is £12,000 * (0.96^5) = £9,830.48. Thus, the correct answer is £9,830.48.

• 5%

• 6.5%

• 7%

• 8%

Answer explanation

The formula V = 1000 × 1.065^n indicates a compound interest rate of 6.5% per annum, as 1.065 represents the growth factor (1 + R/100). Therefore, R = 6.5%.

• £1,500.00

• £1,600.00

• £1,700.00

• £1,750.00

Answer explanation

To find the value after 7 years, substitute n=7 into the formula: V = 1000 × 1.065^7. Calculating this gives V ≈ £1,700.00, which is the correct answer.

• 11 years

• 12 years

• 13 years

• 14 years

Answer explanation

To double her investment, V must equal £2000. Setting up the equation 2000 = 1000 × 1.065^n leads to 2 = 1.065^n. Solving for n gives approximately 11 years, confirming the correct answer is 11 years.

In 2016, there were 10,000 electric cars in the United Kingdom. In 2019, there were 150,000 electric cars. The percentage increase of electric cars, year on year is the same. Assuming the percentage increase remains the same, how many electric cars would you expect there to be in 2021?

• 200,000

• 225,000

• 250,000

• 275,000

Answer explanation

The percentage increase from 10,000 to 150,000 is 1400%. This is a consistent annual growth rate. Applying this rate for two more years (2020 and 2021) results in approximately 250,000 electric cars by 2021.

The number of bacteria in a petri dish grew exponentially. There was 500 in the original bacterial population. After 5 hours, the number increased to 121500. Calculate how many bacteria there was after 8 hours.

• 243,000

• 364,500

• 729,000

• 1,000,000

Answer explanation

The bacteria grow exponentially, so we can use the formula N(t) = N0 * e^(kt). Given N(5) = 121500, we find k, then use it to calculate N(8). This results in N(8) = 729000, which is the correct answer.

A sunflower grows 12% taller each week. Currently the sunflower is 2 m tall. Chris estimates the height after 5 weeks using the following calculation: 12% of 2 m is 24 cm 5 × 24 cm = 120 cm So the plant is 200 cm + 120 cm = 320 cm. Is Chris' estimate an over-estimate or under-estimate?

• Over-estimate

• Under-estimate

Answer explanation

Chris' estimate is an over-estimate because he calculated a fixed 12% of the initial height each week instead of applying the growth to the new height each week, leading to an inflated total height.