Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

During a 3h-experiment, the number of bacteria increased fro

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

During a 3h-experiment, the number of bacteria increased fro

by fskilnik@GMATH » Tue Feb 26, 2019 2:40 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

GMATH practice exercise (Quant Class 12)

Image

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

Answer: [spoiler]____(D)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Wed Feb 27, 2019 7:38 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)

Image

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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Post new topic Post Reply
• Page 1 of 1