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Exponential graphs GCSE lesson: growth, decay and compound interest, y = a × bˣ

Name: ____________________ Date: ____________________

Show your working. Check every root by substitution and label your sketches.

Exponential growth and decay: practice

Write the multiplier first, then the working. Give money to the nearest penny. The stretch is optional.

Diagnostic question: choose and explain

  1. £3000 is invested at 4% compound interest a year. Which works out its value after 5 years?
    1. 3000 × 1.04⁵
    2. 3000 × 1.04 × 5
    3. 3000 + 5 × 120
    4. 3000 × 0.04⁵

Practice questions

  1. The multiplier for a 6% increase is ___, and for a 6% decrease it is ___
  2. £800 is invested at 3% compound interest a year. What is it worth after 2 years? Type the number of pounds to the penny, without the £ sign.
  3. A phone bought for £600 loses 25% of its value each year. What is it worth after 2 years? Type the number of pounds, without the £ sign.
  4. Each table gives y for x = 0, 1, 2, 3. Which shows exponential growth?
    1. 5, 10, 20, 40
    2. 5, 10, 15, 20
    3. 40, 20, 10, 5
  5. Where does the graph of y = 6 × 0.5ˣ cross the y-axis?
    1. (0, 6)
    2. (0, 0.5)
    3. (0, 3)
    4. (0, 0)
  6. Does the graph of y = 6 × 0.5ˣ ever reach 0?
    1. No: half of something is never nothing
    2. Yes, at x = 12
    3. Yes, at x = 0
  7. A town has 20 000 people, and its population grows by 10% a year. After 3 years it has ___ people
  8. Higher: y = a × bˣ goes through (0, 3) and (2, 48), with b positive. a = ___ and b = ___
  9. Stretch: £1000 is invested at 8% compound interest a year. After how many whole years is it first worth more than £2000?

Support: For question 2: 3% up keeps all of it and adds 3%. What do you multiply by for one year? Two years: how many times do you multiply by it?

Exponential growth and decay: exit

The equation, the working, and one sentence.

  1. A bike costs £400 and loses 20% of its value each year. Write its value after x years as y = a × bˣ, and work out its value after 2 years. Will it ever be worth £0? Say why.

Exit check

One depreciation question shows who writes the multiplier and the power, and why it never reaches 0.

A bike costs £400 and loses 20% of its value each year. Write its value after x years as y = a × bˣ, and work out its value after 2 years.

Exponential growth and decay: multipliers, powers and graphs

Write the multiplier before any working. Give money to the nearest penny. Question 6 is for Higher.

1. Write the multiplier for a 7% increase, for a 30% decrease and for a 2.5% increase.

2. £5000 is invested at 3% compound interest a year. Work out its value after 4 years.

3. A car bought for £16 000 loses 12% of its value each year. Work out its value after 3 years.

4. Complete a table for y = 2 × 3ˣ for x = 0, 1, 2, 3, then draw the graph.

5. £1000 is saved for 3 years at 5% a year. Work out its value with simple interest and with compound interest. Which is more, and why?

6. The graph of y = a × bˣ goes through (0, 80) and (2, 20), with b positive. Find a and b, then the value of y when x = 3.

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