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Question

City  growth and a number of traffic signal for a certain city are related by a linear equation. Records show  that there were 50 traffic signal when a local population was 25,000 and that the rate of increase in the number of traffic signals was 1 for every 1,000 new residents.

1) using p for population and T for traffic write an equation (in slope -intercept form) that the transportation department can use to predict future traffic signal needs.

2) how many traffic signal can be expected when the population reaches 35,000

Answer 1

1)

City  Population = p

Number of traffic signals = T.

An equation in slope -intercept form is T = mp + c.            -------------------- (1)

The rate of increase in the number of traffic signals was 1 for every 1,000 new residents.

Slope m = 1/1000

When a local population was 25,000 , traffic signals are 50.

Substitute : p = 25000 , T = 50 , m = 1/1000

50 = 25 + c

c = 50 - 25

c = 25

 

Equation (1)   :   T = mp + c

Substitute : c = 25 , m = 1/1000

Solution :

Answer 2

2)

When the population reaches 35,000  ⇒  p = 35000

Number of traffic signals = T = ?

Substitute : p = 35000.

T = 35 + 25

T = 60

Solution :

The traffic signal "60" when the population reaches 35,000.