Question

A town has an initial population of 75,000 in 2010. It grows at a constant rate of 2,500 per year for 5 years.Find the linear function that models the town’s population P as a function of the year, T where t is the number of years since the model began. Type your answer in slope intercept form (y=mx+b) without any commas or spaces and be sure to use lower case letter for your variable and t.The linear function is P(t)=AnswerThe x-intercept is (Answer,Answer)The y intercept is (Answer,Answer)The population will reach 100,000 in the year Answer

Answer 1

The initial population = 75,000 in 2010

It grows at a constant rate of 2,500 per year for 5 years

If the linear function is P(t),

`P(t)\text{ = }2500x\text{ + 75,000}`

The x - intercept is;

`\begin{gathered} 2500x\text{ + 75,000 = 0} \\ 2500x\text{ = -75,000} \\ x\text{ = }\frac{-\text{ 75,000}}{2500} \\ \\ x\text{ = - 30} \\ x\text{ - intercept is ( -30, 0)} \end{gathered}`

The y - intercept is (0, 75000).

We are now to find when the population will reach 100,000.

`\begin{gathered} 2500x\text{ + 75,000 = 100,000} \\ 2500x\text{ = 100,000 - 75,000} \\ 2500x\text{ = 25,000} \\ x\text{ = }(25000)/(2500) \\ x\text{ = 10 } \end{gathered}`

It will take the town 10 years for its population to reach 100,000, i.e in the year 2020 but we can not conclude because the g