A beam of light with an initial intensity of 80 W/m2 enters a slab of

Question

https://gmatclub.com/forum/download/file.php?id=89611 A beam of light with an initial intensity of 80 W/m^2 (watts per square meter) enters a slab of a particular material. For distances from 0 to 40 centimeters through the material, the intensity I of the light, in W/m^2, is accurately modeled by the equation I = N * 2^{(-kd)} , whose graph is given. Here, N and k are positive constants, and d is the distance, in centimeters, that the light has traveled through the material. When d = 0, I represents the initial intensity of the light immediately before it enters the material. From each drop-down menu, select the option that creates the most accurate statement based on the information provided. The constant k is equal to GRAPH_1_PLACEHOLDER . If the model continues to be accurate for distances greater than 40 centimeters, the light intensity after traveling 55 centimeters through the material will be GRAPH_2_PLACEHOLDER of the light intensity after traveling 15 centimeters through the material. GMAT-Club-Forum-0zq5qkbz.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=89611

A beam of light with an initial intensity of 80 W/m^2 (watts per square meter) enters a slab of a particular material. For distances from 0 to 40 centimeters through the material, the intensity I of the light, in W/m2, is accurately modeled by the equation  I = N * 2^{(-kd)} , whose graph is given. Here, N and k are positive constants, and d is the distance, in centimeters, that the light has traveled through the material. When d = 0, I represents the initial intensity of the light immediately before it enters the material.

From each drop-down menu, select the option that creates the most accurate statement based on the information provided.

The constant k is equal to  GRAPH_1_PLACEHOLDER .

If the model continues to be accurate for distances greater than 40 centimeters, the light intensity after traveling 55 centimeters through the material will be  GRAPH_2_PLACEHOLDER  of the light intensity after traveling 15 centimeters through the material.

Official Solution:  
 
Drop-down 1:

From the graph, the light intensity is 80 W/m^2 at d = 0 and 40 W/m^2 at d = 10.

So increasing the distance through the material by 10 centimeters cuts the intensity in half.

According to the model,

I = N * 2^{(-kd)}

so increasing d by 10 multiplies the intensity by

2^{(-10k)}

Since the intensity is halved,

2^{(-10k)} = \frac{1}{2} = 2^{(-1)}

Therefore,

10k = 1

k = 0.10

So the correct answer is  0.10 .
 
Drop-down 2:

We are comparing the light intensity after 55 centimeters with the light intensity after 15 centimeters.

The difference is

55 - 15 = 40 centimeters

From the graph and the model, every additional 10 centimeters cuts the intensity in half.

So an additional 40 centimeters means the intensity is multiplied by

(1/2) * (1/2) * (1/2) * (1/2) = 1/16

Therefore, the light intensity after traveling 55 centimeters through the material will be  1/16  of the light intensity after traveling 15 centimeters through the material.
 
Correct answer:  
Drop-down 1: "0.10"
Drop-down 2: "1/16"

aditya1818 · Answer

Bunuel

Please check for the second combination options. I am getting 1/16 and it is not present in the option. I think there is a typo error in the option.

Bunuel · Answer

Edited the typo. Thank you.

kaustubhkohli12 · Answer

Value of constant k = 0.10 and second option is 1/16 . Can someone confirm ?

Panay · Answer

Can someone please show how are we arriving at these answers?

Jyoti3380 · Answer

Using the given formula:

For Q1: What's K? 
Sol: Take any two intensity points and with their given distance, equate them. You will arrive at K = 1/10

For Q2: We need to equate both the equations i.e., (Eq1: When D=55) = A (Eq2: When D=15)

"A" is the fraction which is asked in the question.

I solved this one with approximation; When D=15, I= 30 and D=55, I= will be less than 2.5. Next, just equate them and you will get A= 25/(30*10); which is  1/12.  Now out of the dropdown options; closest is 1/16.

So yes, that is how I approached this question.

PS: I wanted to paste my solution picture, but it is too embarrassing;

Points which may help: Don't use LOG (I tried and it was of no help); though it is clearly mentioned N and K are +ve constants; just take care of it and else we may do silly mistakes.

SwiftMonk · Answer

the intensity unit in w per meter square and the distance it is in cm, makes it trickier

Jash1666 · Answer

For this difficulty level what should be ideal time for solving and above that we should move ahead.

A beam of light with an initial intensity of 80 W/m2 enters a slab of

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