Answer:
2002.7 (1 d.p.).
The value of the exports reached $8.8 billion during the year 2002.
Step-by-step explanation:
The function modelling the approximate value of China's exports of automobiles and parts (in billions of dollars) is:
[tex]f(x)=1.8208e^{0.3387x}[/tex]
where x = 0 corresponds to 1998.
To find the year when the exports reach $8.8 billion, substitute f(x) = 8.8 into the given equation, solve for x, then add this value to 1998.
[tex]\begin{aligned}1.8208e^{0.3387x}&=8.8\\\\e^{0.3387x}&=\dfrac{8.8}{1.8208}\\\\\ln e^{0.3387x}&=\ln \left(\dfrac{8.8}{1.8208}\right)\\\\0.3387x&=\ln \left(\dfrac{8.8}{1.8208}\right)\\\\x&=\dfrac{\ln \left(\dfrac{8.8}{1.8208}\right)}{0.3387}\\\\x&=4.65153751...\end{aligned}[/tex]
Add the found value of x to the year 1998:
[tex]\implies 1998+4.65153751...=2002.65153...[/tex]
Therefore, the the value of the exports reached $8.8 billion during the year 2002.
As the answer requires the year with at least one decimal place, the final answer is 2002.7 (1 d.p.).
