GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Mar 2019, 20:56

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

During a 3h-experiment, the number of bacteria increased from 10^4 (at

Author Message
TAGS:

Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 902
During a 3h-experiment, the number of bacteria increased from 10^4 (at  [#permalink]

Show Tags

26 Feb 2019, 15:48
00:00

Difficulty:

55% (hard)

Question Stats:

50% (03:01) correct 50% (02:06) wrong based on 10 sessions

HideShow timer Statistics

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

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 902
Re: During a 3h-experiment, the number of bacteria increased from 10^4 (at  [#permalink]

Show Tags

27 Feb 2019, 08:50
fskilnik wrote:
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

$$f\left( t \right) = a \cdot {b^t}\,\,\,{\rm{bacteria}}\,\,\,\,\,\left( {{\rm{at}}\,\,t \ge 0\,\,{\rm{hours}}} \right)$$

$$? = f\left( {{1 \over 2}} \right) = a \cdot \sqrt b$$

$$\left( {0\,;\,{{10}^4}} \right) \in \,\,{\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,{10^4} = a \cdot {b^0} = a\,\,\,\,\left( * \right)$$

$$\left( {3\,;\,8 \cdot {{10}^4}} \right) \in \,\,{\rm{graph}}\left( f \right)\,\,\,\,\, \Rightarrow \,\,\,\,8 \cdot \,{10^4}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{10^4} \cdot {b^3}\,\,\,\, \Rightarrow \,\,\,\,b = 2$$

$$?\,\, = \,\,{10^4} \cdot \sqrt 2 \,\, \cong \,\,1.41 \cdot {10^4} = 14100\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{D}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: During a 3h-experiment, the number of bacteria increased from 10^4 (at   [#permalink] 27 Feb 2019, 08:50
Display posts from previous: Sort by