A random assortment of maths problems with recurring characters.
Percentage error
![A boy says 'guess my height' and a girl replies '165cm?'
Behind there is a tape measure indicating that he is actually 160cm tall.](img/percentage_error_1.png)
Lily estimates Aarav's height to be 165cm.
Actually he is 160cm tall.
The error in her estimate is the difference:
error = 165cm - 160cm = 5cm
The percentage error is the error, 5cm, as a percentage of the actual height, 160cm:
percentage error = 5160× 100%
= 3.125%
![A magpie says 'guess my height' and a noisy miner bird replies '45cm?'
Behind there is a tape measure indicating that the magpie is actually 40cm tall.](img/percentage_error_2.png)
Now, suppose a noisy miner bird estimates a magpie's height as 45cm.
If the magpie is actually 40cm tall, again the error is 5cm:
error = 45cm - 40cm = 5cm
What is the percentage error?
Exponential Growth
![One night, Rowan made a video of a possum in a toy shop.](img/exponential_growth_1.png)
![Ten minutes later, he shared the video with three friends.](img/exponential_growth_2.png)
![Ten minutes after that, they each shared the video with three more friends.](img/exponential_growth_3.png)
If the sharing continues at this rate,
how many people will have seen the video after one hour?