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