# To the power of n

## Lesson details

### Key learning points

1. 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.

## Video

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## Worksheet

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## Starter quiz

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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).
Correct answer: \$1,040.98 (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)
Correct answer: £84.86 (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)
Correct answer: £1.11 (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

## Exit quiz

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### 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
Correct answer: a = 3, b = 4
a = 3, b = 7
Q4.
y = 9^x would cut the y-axis at the coordinate...