Rewrite the equation in terms of base $e$. Express the answer in terms of a natural logarithm and then round to three decimal places.
\[
y=109(4.9)^{x}
\]
Express the answer in terms of a natural logarithm.
\[
y=
\]
(Do not simplify.)
Simplify the answer, rounding to three decimal places.
\[
y=
\]

Step 1 ：Rewrite the equation in terms of base \(e\). Using the property of logarithms that states \(a^b = e^{b \ln a}\), we can rewrite the equation as \(y = 109e^{x \ln 4.9}\).

Step 2 ：Express the answer in terms of a natural logarithm. The natural logarithm is the logarithm to the base \(e\), denoted as \(\ln\). So, the equation remains the same.

Step 3 ：Simplify the answer, rounding to three decimal places. This involves calculating the value of \(\ln 4.9\) and multiplying it by \(x\).

Step 4 ：\(\ln 4.9\) is approximately 1.589.

Step 5 ：Substitute this value into the equation to get \(y = 109e^{1.589x}\).

Step 6 ：\(\boxed{y = 109e^{1.589x}}\) is the final answer.