Question

As part of a laboratory experiment, the number of times a light is flashed on a certain culture of bacteria is reduced $20$ percent each day. If the light flashed $704$ times on the fourth day of the experiment, then the number of times it flashed on the first day is closest to

• A. $880$
• B. $1,217$
• C. $1,267$
• D. $1,375$
• E. $1,460$

Answer 1

The correct option is D $1,375$

Given that in laboratory experiment, the number of times a light flashed on certain culture of bacteria is reduced $20\%$.

Hence, the number of times light is flashed on the next day will be $(1-\frac{20}{100})=(1-0.2)=0.8$ times the light flashed on the present day.

Then first day: $100$ to $0.8\times 100=80$

Second day: $80$ to $0.8\times 80=64$

Third day: $64$ to $0.8\times 64=51.20$

And fourth day $51.20$ to $0.8\times 51.20=40.96$

Then bacteria reduced fourth day $=51.20-40.96=10.24$

Then light is flashed first day $=$ $\frac{20}{10.24}\times 704=1375$