24.5k views
4 votes
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 $8.8 billion?



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

1 Answer

6 votes

Answer:

2002.7 (1 d.p.).

The value of the exports reached $8.8 billion during the year 2002.

Explanation:

The function modelling the approximate value of China's exports of automobiles and parts (in billions of dollars) is:


f(x)=1.8208e^(0.3387x)

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.


\begin{aligned}1.8208e^(0.3387x)&=8.8\\\\e^(0.3387x)&=(8.8)/(1.8208)\\\\\ln e^(0.3387x)&=\ln \left((8.8)/(1.8208)\right)\\\\0.3387x&=\ln \left((8.8)/(1.8208)\right)\\\\x&=(\ln \left((8.8)/(1.8208)\right))/(0.3387)\\\\x&=4.65153751...\end{aligned}

Add the found value of x to the year 1998:


\implies 1998+4.65153751...=2002.65153...

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.).

The value of China's exports of automobiles and parts (in billions of dollars) is-example-1
User Redson
by
7.8k points