the population P (in 1000s) of a town can be modeled by P = 2 absolute value t-5 +6, where t = 0 represent 1990. During which two years does the town have a population of 12,000?
To find the two years during which the town has a population of 12,000, we can substitute the given population value into the equation and solve for "t."
Given: P = 12,000
Substituting this into the equation, we get:
12,000 = 2|t - 5| + 6
Now, let's solve for "t":
12,000 - 6 = 2|t - 5|
11,994 = 2|t - 5|
To eliminate the absolute value, we can split the equation into two cases, one with the expression inside the absolute value being positive and the other with it being negative:
Case 1: t - 5 > 0
Simplifying and solving for "t," we have:
11,994 = 2(t - 5)
11,994 = 2t - 10
2t = 11,994 + 10
2t = 12,004
t = 12,004 / 2
t = 6,002
Case 2: t - 5 < 0
Simplifying and solving for "t," we have:
11,994 = 2(-t + 5)
11,994 = -2t + 10
2t = 11,994 - 10
2t = 11,984
t = 11,984 / 2
t = 5,992
Therefore, the two years during which the town has a population of 12,000 are 1996 (t = 6,002 represents 1996) and 1992 (t = 5,992 represents 1992), considering that t = 0 represents 1990.