Question

The population, P (in thousands), of a town can be modeled by P= 2|t-6|+4, where t=0 represents 1990. During which two years does the town have a population of 8000?

Can someone show me the steps to this problem?

Answer 1

P = 2 * | t - 6 | + 4 = 8

( Remark : 8 mean 8 thousands )

2 * | t - 6 | = 8 - 4

2 * | t - 6 | = 4 Divide both sides with 2

| t - 6 | = 2



| t - 6 | = t - 6


and


| t - 6 | = - ( t - 6 ) also


You must solve two equations:

1.)

t - 6 = 2

t = 2 + 6

t = 8


and

2.)

- ( t - 6 ) = 2

- t + 6 = 2

- t = 2 - 6

- t = - 4 Multiply both sides with - 1

t = 4


So equation:

P = 2 * | t - 6 | + 4 = 8

has the two solutions :

t = 4 yrs

and

t= 8 yrs


Proof:

P = 2 * | t - 6 | + 4

for t = 4 yrs

P = 2 * | 4 - 6 | + 4 =

2 * | - 2 | + 4 =

2 * 2 + 4 =

4 + 4 = 8



P = 2 * | t - 6 | + 4

for t = 8 yrs

P = 2 * | 8 - 6 | + 4 =

2 * | 2 | + 4 =

2 * 2 + 4 =

4 + 4 = 8

Answer 2

1990 + 4 = 1994 yr


1990 + 8 = 1998 yr

Answer 3

Thank you so much!!

Answer 4

Your welcome its no problem