Question

the sun releases 3.85×10²⁶ joules of energy every second. according to the e.i.a., the u.s. consumed about 1.03×10²⁰ joules of energy in 2011. if the u.s. continues at that rate of consumption, how many years could one second of energy from the sun power the u.s.?

Explanation:

Step1: Calculate the number of seconds of U.S. energy - consumption

We divide the energy released by the sun in one - second by the U.S. annual energy consumption. Let $E_{sun}=3.85\times 10^{26}$ J (sun's one - second energy release) and $E_{US}=1.03\times 10^{20}$ J (U.S. annual energy consumption). The number of years $n$ is given by the ratio of the sun's one - second energy to the U.S. annual energy consumption. First, calculate the number of seconds of U.S. energy consumption from the sun's one - second energy: $\frac{E_{sun}}{E_{US}}=\frac{3.85\times 10^{26}}{1.03\times 10^{20}}$.
Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{3.85}{1.03}\times10^{26-20}\approx3.74\times 10^{6}$ seconds.

Step2: Convert seconds to years

We know that there are $365\times24\times3600 = 31536000=3.1536\times 10^{7}$ seconds in a year.
To convert the number of seconds to years, we divide the number of seconds by the number of seconds in a year. Let $t$ be the number of years, then $t=\frac{3.74\times 10^{6}}{3.1536\times 10^{7}}$.
Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we get $t=\frac{3.74}{3.1536}\times10^{6 - 7}\approx0.119\times10^{-1}= 0.0119$ years.

Answer:

$0.0119$ years