The population of Sasquatch in Salt Lake County was modeled by the function $P(t)=\frac{500 t}{t+50}$, where $t=0$ represents the year 1803. When were there fewer than 100 Sasquatch in Salt Lake County? Present your answer, to the nearest whole year, in interval notation. There were fewer than 100 Sasquatch in Salt Lake City between the years

Step 1 ：Set up the inequality: \(\frac{500 t}{t+50} < 100\)

Step 2 ：Multiply both sides by (t+50) to get rid of the denominator on the left side: \(500t < 100(t + 50)\)

Step 3 ：Simplify the inequality: \(500t < 100t + 5000\)

Step 4 ：Subtract 100t from both sides: \(400t < 5000\)

Step 5 ：Divide both sides by 400: \(t < 12.5\)

Step 6 ：Add 12.5 to 1803 to find the year: \(1803 + 12.5 = 1815.5\)

Step 7 ：Round up to the nearest whole year: 1816

Step 8 ：The interval notation is represented as (1803, 1816)

Step 9 ：\(\boxed{1816}\) is the year before which there were fewer than 100 Sasquatch in Salt Lake County