Question

An amusement park opens daily at 9:30 a.m. This morning the parking lot for the amusement park opened at 8:00 a.m. At 9:00 a.m., there were 132 cars in the parking lot. The parking attendants noticed that every half hour between 9:00 a.m. and 10:30 a.m., the number of cars in the parking lot tripled. What type of function appropriately models this situation?

Answer 1

9:00 am

Explanation:

Answer 2

An exponential function

Explanation:

So let's suppose that at 9:00 am there were 132 cars. We'll call this
`P_0`

`P_(0)=132`

On the next half an hour, let's say at 9:30, the number of cars trippled, this is:

`P_(1)=132*3=396`

the next half an hour, at 10:00 am, the number of cars trippled, this is:

`P_(2)=132*3*3=1188`

and finaly, at 10:30am, the number of cars trippled again, so:

`P_(3)=132*3*3*3=3564`

We can now see a pattern there which can be simplified as:

`P(n)=P_(0)(3)^(n)`

or

`P(n)=132(3)^(n)`

where:

`P_(0)=`initial number of cars

n=number of half hours after 9:00 a.m

`P_(n)=` number of cars after n number of half hours.

That function we found there is an exponential function, which represents an initial amount being multiplied by the same number several times.