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?

An exponential function

Step-by-step explanation:

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

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

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

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

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

or

where:

initial number of cars

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

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.

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step-by-step explanation: