Answer:
t=17.61 years.
Step-by-step explanation:
Given that
Reserve of energy = 10,000 EJ
Energy used by human = 18 TW
We know that
![1\ E= 10^(18)](https://img.qammunity.org/2020/formulas/geography/college/y7m6gsiujchbt785eocedf2kp3gj847i5x.png)
![1\ T= 10^(12)](https://img.qammunity.org/2020/formulas/geography/college/p1wsoh614uj3fijjh91fg8xu7t0t2p8zsu.png)
So
![Reserve\ of\ energy = 10,000 *10^(18) J](https://img.qammunity.org/2020/formulas/geography/college/m76db1zublmbsbghpmssmcs44urdzsjt4x.png)
![Reserve\ of\ energy = 10^(22) J](https://img.qammunity.org/2020/formulas/geography/college/5s7r0vduhwhmqjfh370wzr9ij5wmsu8lwk.png)
![Energy\ used\ by\ human = 18 *10^(12)\ W](https://img.qammunity.org/2020/formulas/geography/college/2wrr1y3npwydl64lk25h80wk8lgkfbhzlg.png)
Lets t time after energy will be exhaust
So
![18 *10^(12)* t=10^(22)](https://img.qammunity.org/2020/formulas/geography/college/tfg5xtegvp70pslq83hlq8ynmarttoorl4.png)
![t=(10^(22))/(18 *10^(12))\ s](https://img.qammunity.org/2020/formulas/geography/college/zowp6dezm6jyk9vko5ejvkk1mftuhgq5z1.png)
![t=5.55* 10^8 \ s](https://img.qammunity.org/2020/formulas/geography/college/8hellayk6p43c8ahmzjxmi3y74fll5njmc.png)
We know that
1 year = 365 days
1 year = 365 x 24 hr
1 year = 365 x 24 x 3600 s
![1year =3.15* 10^7\ s](https://img.qammunity.org/2020/formulas/geography/college/cvnhnzz5w8lfwghx97a7lwli8g5ves4dvt.png)
So
![t=(5.55* 10^8 )/(3.15* 10^7)](https://img.qammunity.org/2020/formulas/geography/college/v3sdds5u5v5ugp3k9680jjqo1djf4nrusa.png)
t=17.61 years.