A towns' population, P(x), is given by the function P(x) =2700x + 21000 where x represents the years since 2003.
The population will reach 83,400 in ______
The population in 2010 will be ______
2700x+21000 = 83400
just solve for x
2010 is 7 years after 2003, so just plug in x=7 for P(x)
thanks!!
To find the year when the population reaches 83,400, we need to set P(x) equal to 83,400 and solve for x.
The given function is P(x) = 2700x + 21000.
So, we substitute 83,400 for P(x):
83,400 = 2700x + 21000
To solve for x, we need to isolate it on one side of the equation:
83,400 - 21,000 = 2700x
62,400 = 2700x
Now, divide both sides of the equation by 2700:
62,400 / 2700 = x
x ≈ 23.11
Therefore, the population will reach 83,400 in approximately 23.11 years after 2003. To determine the year, we need to add x to 2003:
2003 + 23.11 ≈ 2026.11
So, the population will reach 83,400 in the year 2026.
To find the population in 2010, we need to substitute x = 2010 - 2003 = 7 into the given function:
P(7) = 2700(7) + 21,000
P(7) = 18,900 + 21,000
P(7) = 39,900
Therefore, the population in 2010 will be 39,900.