Exponential Functions

A=P(X)^t/n

A-final amount
P-initial amount
X-growth rate
t-time
n-number of growth periods

The teacher had this question as an example and did it however i do not understand one thing:

The Ebola virus double every 30 min. If there are currently 2000 ebola viruses present in petrie dish, how many are present in 7 hours from now?

A=2000(2)^7/0.5 = 32768000

^ What I don't get about that is where he got the 0.5 from? Isnt it supposed to be 30 min? so 30? cause that's the growth period :|

Your exponents should have been defined in hours

so 30 minutes = 30/60 hours = 1/2 or 0.5 hours

it says, the virus doubles every 30 minutes
so how do you "double" something? Don't you multiply by 2 ?

so the fixed part of the equation is
A = 2000(2)^(t/.5)

your only input is t, namely the number of hours you are dealing with
suppose we look at 2 hours , so after
30 minutes we have 4000 , after
60 minutes we have 8000 , after
90 minutes we have 16000, after
120 minutes we have 32000

and 2000(2)^(2/.5)
= 2000(2^4)
= 2000(16)
= 32000

I think n is poorly defined.
I would have defined n as the doubling period expressed in hours.

Oh so they always have to be in hours? growth periods are always in hours?

In the formula A = P(X)^(t/n), where A is the final amount, P is the initial amount, X is the growth rate, t is the time, and n is the number of growth periods, it seems like your teacher made an error in using the wrong value for "n".

In this example, "n" would represent the number of growth periods within the given time frame, which is 7 hours. Since the Ebola virus doubles every 30 minutes, we need to find the number of growth periods within 7 hours and express it in terms of 30-minute intervals.

To convert the 7-hour time period into 30-minute intervals, we need to divide it by 30 minutes. So, 7 hours is equal to 7 * 60 minutes, which gives us 420 minutes.

To find the number of growth periods within 420 minutes, we divide 420 by 30: 420 / 30 = 14.

So, the correct calculation should be:

A = 2000(2)^(7/14) = 2000(2^0.5) = 2000(√2) ≈ 2000(1.414) ≈ 2828

Therefore, approximately 2828 Ebola viruses would be present in the petri dish after 7 hours.

It seems like your teacher used 0.5 as the value for "n" unintentionally, but it should have been 14 in this case.