1.Carbon-14 (¹⁴C) dating assumes that the carbon dioxide on the Earth today has the same radioactive content as it did centuries ago. If this is true, then the amount of¹⁴C absorbed by a tree that grew several centuries ago should be the same as the amount of¹⁴C absorbed by a similar tree today. A piece of ancient charcoal contains only13%as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The half-life of¹⁴C is 5715 years. Round your answer to one decimal place.)

2.A small business assumes that the demand function for one of its new products can be modeled byp=Ce^kx.

Whenp=$50,x=800units, and whenp=$40,x=1200units.(a) Solve forCandk. (RoundCto four decimal places andkto seven decimal places.)

C	=
k	=

(b) Find the values ofxandpthat will maximize the revenue for this product. (Roundxto the nearest integer andpto two decimal places.)

x	=	units
p	=	$