# Pre-Calculus

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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 :|

• Pre-Calculus - ,

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.

• Pre-Calculus - ,

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