# Exponential growth

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## Lesson details

### Key learning points

- In this lesson, we will learn about the exponential function and how it relates to powers of n.

### 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 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

### 5 Questions

Q1.

Starting with 100 bacteria, how many would there be after 1 hour if the number of bacteria increases by 20% every 12 minutes?

120

248

249

Q2.

Which of the following is the closest approximation to e?

2.7

2.7182

3.14

Q3.

If a bacterium increases by 1% in 2 minutes, would this form an exponential curve?

No

Q4.

What is the coordinate of intersection with the y-axis for y = e^x?

(0, 0)

(1,0)

y = 1

Q5.

If an investment doubled every 3 years, would the growth of the investment form an exponential curve?

No