12. Karen is going to raise money for a charity.
She aims to cycle a total distance of 1000 km over a number of days.
On day one she cycles 25 km .
She increases the distance that she cycles each day by \(10 \%\) of the distance cycled on the previous day, until she reaches the total distance of 1000 km .
She reaches the total distance of 1000 km on day \(N\), where \(N\) is a positive integer.
- Find the value of \(N\).
On day one, 50 people donated money to the charity. Each day, 20 more people donated to the charity than did so on the previous day, so that 70 people donated money on day two, 90 people donated money on day three, and so on.
- Find the number of people who donated to the charity on day fifteen.
Each day, the donation given by each person was \(\pounds 5\)
- Find the total amount of money donated by the end of day fifteen.