Answer:there were fewer than 150 Sasquatch in Salt Lake County before the year 1824.
Explanation:
To determine when there were fewer than 150 Sasquatch in Salt Lake County, we need to find the values of T that make the population function, P(T), less than 150.
The population function is given by P(T) = 500T / (T + 50), where T represents the number of years since 1803.
To solve for T when P(T) is less than 150, we set up the inequality:
500T / (T + 50) < 150
To solve this inequality, we can multiply both sides by (T + 50) to get rid of the denominator:
500T < 150(T + 50)
Next, we distribute the 150 to both terms inside the parentheses:
500T < 150T + 7500
Combining like terms, we have:
500T - 150T < 7500
Simplifying further, we get:
350T < 7500
To isolate T, we divide both sides of the inequality by 350:
T < 7500 / 350
Calculating the division, we find:
T < 21.43
Since T represents the number of years since 1803, we round down to the nearest whole number to find the earliest year when there were fewer than 150 Sasquatch. Thus, T < 21.
To determine the year, we add T to 1803:
Year < 21 + 1803
Year < 1824
Therefore, there were fewer than 150 Sasquatch in Salt Lake County before the year 1824.