To find out how long \(6.02 \times 10^{23}\) dollars would last if spent at a rate of $1.00 per second, we can start by calculating the total number of seconds in a year.
First, let's calculate the number of seconds in one year:
\[ \text{Seconds per year} = 365 , \text{days/year} \times 24 , \text{hours/day} \times 60 , \text{minutes/hour} \times 60 , \text{seconds/minute} \]
Calculating that:
\[ \text{Seconds per year} = 365 \times 24 \times 60 \times 60 = 31,536,000 , \text{seconds/year} \]
Now, we can find out how many years the money would last by dividing the total amount of money by the number of seconds per year:
\[ \text{Years} = \frac{6.02 \times 10^{23} , \text{dollars}}{31,536,000 , \text{seconds/year}} \]
Calculating that:
\[ \text{Years} \approx \frac{6.02 \times 10^{23}}{3.1536 \times 10^7} \]
To perform the division:
\[ \frac{6.02 \times 10^{23}}{3.1536 \times 10^7} \approx 1.91 \times 10^{16} , \text{years} \]
Thus, the final result is:
\[ \text{Years} \approx 1.91 \times 10^{16} , \text{years} \]
The correct answer is:
b) \(1.91 \times 10^{16}\) years