# To the power of n

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## Lesson details

### Key learning points

- In this lesson, we will learn about 'to the power of n'. We will invesigate patterns of exponential growth as the value of n increases for any given base.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 5 Questions

Q1.

If an investment of $500.00 increases by 13% per year for 6 years, the amount it would be at the end of the 6 years would be...

$1,040.97 (to the nearest cent).

$578.00 (to the nearest cent).

$825.00 (to the nearest cent).

Q2.

£100.00 decreases by 5% in one year, followed by an increase of 5% in the next year, and then decreases again by 2% for 8 years. What would the final amount be?

£100.00 (to the nearest penny)

£84.00 (to the nearest penny)

£84.87 (to the nearest penny)

Q3.

If a teddy bear depreciates from £3.00 by 18% per year for 5 years, what is the final value of the teddy bear?

£1.10 (to the nearest penny)

£1.12 (to the nearest penny)

£2.10 (to the nearest penny)

Q4.

In order to decrease an amount by 19% for 2 years, I would need to multiply the amount by 0.19^2

True

Q5.

In order to increase an amount by 7.5% for 3 years, I would need to multiply the amount by 1.075^3

False

### 5 Questions

Q1.

If y = 2^n, what is the value of y when n = 5?

1

10

2

Q2.

If y = 5^n, what is the value of y when n = -3?

-1/125

-125

125

Q3.

You are given that 6^a < 220 < 6^b and that 'a' and 'b' are consecutive integers. What are the values of 'a' and 'b'?

a = 1, b = 4

a = 2, b = 3

a = 3, b = 7

Q4.

y = 9^x would cut the y-axis at the coordinate...

(1,0)

y = 1

y = 9

Q5.

y = 2x is an example of an exponential.

True