Question

Help please!
The cost of a parking ticket at IU is $35 for the first offense, but the cost triples for each additional offense. Write a formula for the cost C as a function of the number of tickets n.

Answer 1

Let's work it out.
First offence(n=1): P=35
Second offence(n=2): P=35*3
Third offence(n=3): P=(35*3)*3=35*3²
Fourth offence(n=4): P=(35*3²)*3=35*3³

Now we can see that the power of three each is n-1, so we can a general function for the cost, C:
\[C=35\times3^{n-1}\]

Answer 2

Ticket number Amount Power form
1 $35 $35
2 $35 * 3 $35 * 3^1
3 $35 * 3 * 3 $35 * 3^2
4 $35 * 3 * 3 * 3 $35 * 3^3 (notice exponent is 1
less than ticket number)
... ... ...
n $35 * 3^(n - 1)

Answer 3

Both of you are legends! Thanks for the help, it is greatly appreciated.

Answer 4

You're welcome.