Answer:
Correct option is E
Explanation:
a) 2n^2+2^n operations are required for a text with n words
Thus, number of operations for a text with n=10 words is 2\cdot 10^2+2^{10}=1224 operation
Each operation takes one nanosecond, so we need 1224 nanoseconds for Jim's algorithm
b) If n=50, number of operations required is 2\cdot 50^2+2^{50}\approx 1.12589990681\times 10^{15}
To amount of times required is 1.12589990681\times 10^{15} nanoseconds which is
1125899.90685 seconds (we divided by 10^{9}
As 1$day$=24$hours$=24\times 60$minutes$=24\times 60\times 60$seconds$
The time in seconds, our algortihm runs is \frac{1125899.90685}{24\cdot 60\cdot 60}=13.0312 days
Number of days is {\color{Red} 13.0312}
c) In this case, computing order of number of years is more important than number of years itself
We note that n=100 so that 2(100)^2+2^{100}\approx 1.267650600210\times 10^{30} operation (=time in nanosecond)
Which is 1.267650600210\times 10^{21} seconds
So that the time required is 1.4671881947\times 10^{16} days
Each year comprises of 365 days so the number of years it takes is
\frac{1.4671881947\times 10^{16}}{365}=4.0197\times 10^{13} years
That is, 40.197\times 10^{12}=$Slightly more than $40$ trillion years$
