Question

question 7
0/5 pts 2 98 details
the value of chinas exports of automobiles and parts (in billions of dollars) is approximately $f(x)=1.8208e^{.3387x}$, where $x = 0$ corresponds to the beginning of 2019.
in what year did/will the exports reach $11.5 billion?
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question 8

Explanation:

Step1: Set up the equation

Set \( f(x)=11.5 \), so \( 11.5 = 1.8208e^{0.3387x} \).

Step2: Solve for \( e^{0.3387x} \)

Divide both sides by \( 1.8208 \): \( \frac{11.5}{1.8208}=e^{0.3387x} \).
Calculate \( \frac{11.5}{1.8208}\approx6.316 \), so \( 6.316 = e^{0.3387x} \).

Step3: Take the natural - logarithm of both sides

Using the property \( \ln(e^{a}) = a \), we have \( \ln(6.316)=0.3387x \).
Since \( \ln(6.316)\approx1.843 \), then \( 1.843 = 0.3387x \).

Step4: Solve for \( x \)

Divide both sides by \( 0.3387 \): \( x=\frac{1.843}{0.3387}\approx5.44 \).

Answer:

Since \( x = 0 \) corresponds to the beginning of 2019, and \( x\approx5.44 \), the year is \( 2019 + 5=2024 \).