Question

On day one,there are 100 particles in a laboratory experiment.On day n,where n≥2,one out of every n particles produces another particle.If the total number of particles in the laboratory experiment increases to 1000 on day m,then m equals

• A. 19
• B. 16
• C. 17
• D. 18

Answer 1

Answer: (A)

19

Answer 2

Given:
-Day one: 100 particles
-Day n (where n≥2): One out of every n particles produces another particle.
We want to find the value of m when the total number of particles reaches 1000 on day m.
Step 1: Day Two
On day two (n=2),half of the 100 particles produce another particle.So,the total becomes 100+50=150 particles.
Step 2: Day Three
On day three (n=3),one-third of the 150 particles produce another particle.So,the total becomes 150+50=200 particles.
Step 3: Day Four
On day four (n=4), one-fourth of the 200 particles produce another particle. So,the total becomes 200+50=250 particles.
We can observe a pattern here.In each step,50 particles are added.
Step 4: Day m
On day m,the total becomes 1000 particles.
From step 1 to step m,50 particles are added in each step.
So,the number of steps from day 1 to day m is:
$[m-1=\frac{1000-100}{50}]$
$[m-1=\frac{900}{50}]$
[m-1=18]
Adding 1 to both sides:
[m=18+1]
[m=19]
Therefore,the value of m when the total number of particles in the laboratory experiment reaches 1000 on day m is 19.