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26 Feb 2019, 15:48
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D
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Difficulty:
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64% (02:22) correct
36%
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wrong
based on 239
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GMATH practice exercise (Quant Class 12)
During a 3h-experiment, the number of bacteria increased from 10^4 (at the start) to 8 times this value (at the end), according to a biological law associated with an exponential function (as shown), where a and b are positive constants. If Madame Curie knows that a certain critical number of bacteria in this experiment is reached at exactly 30 minutes after the experiment begins, which of the following is closest to this critical value?
(A) 20,000 bacteria
(B) 18,000 bacteria
(C) 16,000 bacteria
(D) 14,000 bacteria
(E) 12,000 bacteria
During a 3h-experiment, the number of bacteria increased from 10^4 (at the start) to 8 times this value (at the end), according to a biological law associated with an exponential function (as shown), where a and b are positive constants. If Madame Curie knows that a certain critical number of bacteria in this experiment is reached at exactly 30 minutes after the experiment begins, which of the following is closest to this critical value?
(A) 20,000 bacteria
(B) 18,000 bacteria
(C) 16,000 bacteria
(D) 14,000 bacteria
(E) 12,000 bacteria
27 Feb 2019, 08:50
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fskilnik
\(f\left( t \right) = a \cdot {b^t}\,\,\,{\rm{bacteria}}\,\,\,\,\,\left( {{\rm{at}}\,\,t \ge 0\,\,{\rm{hours}}} \right)\)
\(? = f\left( {{1 \over 2}} \right) = a \cdot \sqrt b\)
\(\left( {0\,;\,{{10}^4}} \right) \in \,\,{\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,{10^4} = a \cdot {b^0} = a\,\,\,\,\left( * \right)\)
\(\left( {3\,;\,8 \cdot {{10}^4}} \right) \in \,\,{\rm{graph}}\left( f \right)\,\,\,\,\, \Rightarrow \,\,\,\,8 \cdot \,{10^4}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{10^4} \cdot {b^3}\,\,\,\, \Rightarrow \,\,\,\,b = 2\)
\(?\,\, = \,\,{10^4} \cdot \sqrt 2 \,\, \cong \,\,1.41 \cdot {10^4} = 14100\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{D}} \right)\)
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
04 Jan 2026, 12:26
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