Question

A bacterial culture, growing exponentially, increases from 200 to 500 grams
in the period from 6a.m. to 9 a.m. How many grams will be present at noon.
​

Answer 1

Given : A bacterial culture, growing exponentially,

increases from 200 to 500 grams in the period from 6  am to 9n am.

To Find : How many grams will be present at noon.

Solution:

f(x) = a(1+r)ˣ

at 6 am  x  = 0     f(0) = 200

at 9 am  x = 3      f(3) = 500

at noon  x  = 6    f(6) = ?

f(0) = a(1 + r)⁰

=> 200  = a

f(3) = 200(1+r)³

=> 500 = 200(1+r)³

=> 5/2  = (1+r)³

f(6) =  200(1+r)⁶

=> f(6) =  200((1+r)³)²

=> f(6) =  200((5/2))²

=> f(6)  = 200 * 25 / 4

=> f(6) = 1250

1250  grams will be present at noon.

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