MATH SOLVE

8 months ago

Q:
# The value of China's exports of automobiles and parts (in billions of dollars) is approximately f ( x ) = 1.8208 e .3387 x , where x = 0 corresponds to 1998. In what year did/will the exports reach $12.3 billion?

Accepted Solution

A:

Answer:So, approximately, China's exports of automobiles and parts reach $12.3 billions in the year 2065.Step-by-step explanation:Given:f(x) = [tex]1.8208e^{0.3387x}[/tex]x = 0 corresponds to 1998We need to find when it achieve $12.3 billions export.12.3 billions = 12,300,000,000Now plug f(x) = 12,300,000,000 12,300,000,000 = [tex]1.8208e^{0.3387x}[/tex]Dividing both sides by 1.8208, we get6,755,272,407.7 = [tex]e^{0.3387x}[/tex]Taking "ln" both sides, we getln(6,755,272,407.7) = 0.3387x22.6335891344 = 0.3387xDividing both sides, by 0.3387x = 66.82When we round off to the nearest whole number, we getx = 67 yearsSo, approximately, China's exports of automobiles and parts reach $12.3 billions in the year 2065 (1998 + 67).