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 $8 billion?



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

Answer 1

Answer:

This was occur sometimes in year 2002.4

Step-by-step explanation:

* Lets explain how to solve the problem

- The value of China's exports of automobiles and parts

  (in billions of dollars) is approximately f(x) = 1.8208 e^(0.3387 x)

# You must pay attention about the function is already calculated in

  billions dollars so you will not multiply the value of f(x) by 10^9 to

  change it to billions

∵ The value of x = 0 at 1998

- Remember that e^(0) = 1

∴ f(0) = 1.8208 e^(0) = 1.8208 billion dollars

- You need to calculate the year that the export reaches 8 billion

∵ f(x) = 1.8208 e^(0.3387 x)

∵ f(x) = 8 billion

∴ 8 = 1.8208 e^(0.3387 x)

- Divide both sides by 1.8208

∴ 4.393673111 = e^(0.3387 x)

- Insert ㏑ in both sides

∴ ㏑(4.393673111) = ㏑[e^(0.3387 x)]

- Remember ㏑(e^n) = n ㏑(e), ㏑(e) = 1, then ㏑(e^n) = n

∴ ㏑(4.393673111) = 0.3387 x

- Divide both sides by 0.3387

∴ x = ㏑(4.393673111) ÷ 0.3387

∴ x = 4.37 ≅ 4.4

- Lets add the number of years to 1998

∴ The year is 1998 + 4.4 = 2002.4

∴ This was occur sometimes in year 2002.4