In 2020, a certain company's net income was $\$ 200,000$. Their net income is projected to increase by $11 \%$ each year. This can be modeled by $f(x)=200,000(1+0.11)^{x}$, where $x$ is the number of years since 2020 . How many years after 2020 will the company's net income be $\$ 800,000$ ? Round your answer to the nearest tenth, if necessary. Answer Keypad Keyboard Shortcuts

Step 1 ：Define the initial net income as \$200,000 and the target net income as \$800,000.

Step 2 ：Define the annual growth rate as 11\%, or 0.11.

Step 3 ：Use the formula for exponential growth to calculate the number of years it will take to reach the target income. The formula is \(x = \frac{\ln(\frac{target\_income}{initial\_income})}{\ln(1 + growth\_rate)}\).

Step 4 ：Substitute the given values into the formula to get \(x = \frac{\ln(\frac{800000}{200000})}{\ln(1 + 0.11)}\).

Step 5 ：Solve the equation to get \(x \approx 13.3\).

Step 6 ：Round the result to the nearest tenth to get \(x \approx 13.3\).

Step 7 ：Final Answer: The company's net income will be \$800,000 approximately \(\boxed{13.3}\) years after 2020.