The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)=1.8208e^.3387x,

Question

The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)=1.8208e^.3387x, where x = 0 corresponds to 1998.

In what year did/will the exports reach $7.7 billion?

 

Give your answer as the year, with at least one decimal place

Answer 1

7.7 = 1.8208e^0.3387x

7.7/1.8208 = e^0.3387x

ln(7.7/1.8208) = lne^0.3387x

ln(7.7/1.8208) = 0.3387x

x = ln(7.7/1.8208)/0.3387

x = 4.3

The year with one decimal? That's silly. The year is 2002.