Explain the effects that a natural disaster, such as a hurricane, will have on GDP.

A natural disaster destroys existing wealth, such as houses, factories, etc. Because the value of existing assets is not a part of GDP, their destruction is not recorded as a loss of GDP. 
After the disaster, there will be two effects on GDP. First, there may be a loss of economic activity because factories have closed down and people have lost their jobs. This will appear as a decline in GDP. Second, their will be an increase in investment, as firms and housholds undertake repairs. This will appear as an increase in GDP.
If the second effect is sufficiently large, a natural disaster will induce an increase in GDP. Clearly, this is not an increase in the standard of living, which serves to show how GDP can in many circumstances be a pretty poor measure of the standard of living.