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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 $7.4 billion?

The value of Chinas exports of automobiles and parts in billions of dollars is approximately f x 18208 e 3387 x where x 0 corresponds to 1998 In what year didwi class=

Respuesta :

We have the following equation:

[tex]f(x)=108208e^{0.3387x}[/tex]

where x denotes the number of years after 1998.

By substituting the given information, we have that

[tex]7.4=1.8208e^{0.3387x}[/tex]

and we need to find x. Then, by dividing both sides by 1.8208, we get

[tex]e^{0.3387x=}4.0641475[/tex]

then by taking natural logarithm to both sides, we obtain

[tex]0.3387x=ln(4.0641476)[/tex]

which gives

[tex]0.3387x=1.4022040[/tex]

then, the number of years after 1998 is:

[tex]\begin{gathered} x=\frac{1.4022040}{0.3387} \\ x=4.13996 \end{gathered}[/tex]

which means 4 years after 1998. Then, by rounding to the nearest year, the answer is 2002.

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