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

Answer:

An exponential function

Step-by-step 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.

Answer 2

Answer:

9:00 am

Step-by-step explanation: