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Exponential growth & decay: IGCSE Mathematics questions with answers Free Exponential growth & decay questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Number. Each question has the answer and the marking points an examiner would look for.
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Exponential growth & decay practice questions Question 1 Structured · 5 marks A* challenge
(a) The value of a car decreases by 20% each year.
[3] (b) Find the number of complete years after which the car is first worth less than half its value when new.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) $18310.550.80 seen B1 5 M1 A1
3 (b) 4trials of 0.80n with at least one value either side of 0.5 M1 A1
2
Question 2 Structured · 7 marks A* challenge
The population of town A is 20000 and increases by 5% each year.
(a) Calculate the population of town A after 5 years, correct to the nearest whole number.
[2] (b) Find the number of complete years after which the population of town A is first greater than the population of town B.
[3] (c) Calculate the population of town B 3 years ago, assuming the same rate of decrease.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) 2552620000 × 1.055 M1 A1
2 (b) 3forms both expressions after n years M1 M1 A1
3 (c) 4115230000 ÷ 0.93 M1 A1
2
Question 3 Structured · 4 marks
(a) A car costs $35000. Its value depreciates by 12% each year. Calculate its value after 4 years.
[2] (b) After how many complete years is the value first less than half of the original value?
[2] Show answers and mark scheme Part Answer and marking points Marks (a) $20989.3435000 × 0.884 M1 A1
2 (b) 6Trial of repeated multiplication M1 A1
2
Question 4 Structured · 4 marks A* challenge
(a) After a 6% increase, a population is 7290. Find the population before the increase.
[2] (b) The population continues to grow by 6% each year. Find the number of years until it first exceeds 14580.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) 6877.47290 ÷ 1.06 M1 A1
2 (b) 12method M1 A1
2
Question 5 Structured · 5 marks A* challenge
(a) The value of a car decreases by 20% each year.
[3] (b) Find the number of complete years after which the car is first worth less than half its value when new.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) $14160.160.80 seen B1 4 M1 A1
3 (b) 4trials of 0.80n with at least one value either side of 0.5 M1 A1
2
Question 6 Structured · 7 marks A* challenge
The population of town A is 12000 and increases by 6% each year.
(a) Calculate the population of town A after 5 years, correct to the nearest whole number.
[2] (b) Find the number of complete years after which the population of town A is first greater than the population of town B.
[3] (c) Calculate the population of town B 3 years ago, assuming the same rate of decrease.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) 1605912000 × 1.065 M1 A1
2 (b) 8forms both expressions after n years M1 M1 A1
3 (c) 4623236000 ÷ 0.923 M1 A1
2
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