Question

Frisco ISD had a student enrollment of approximately 46,000 students in 2013 and is growing at an average rate of about 6% annually. If this rate continues the enrollment growth can be modeled using the equation 46000(1.06)t = y where t represents time in years and y represents number students. How many years will pass until the population of Frisco ISD is at 100,000 students? ≈ 13.33 years ≈ 85.91 years ≈ 5.62 years ≈ 2.05 years

Answer 1

≈ 13.33 years

Explanation:

The population of Frisco ISD after t years is given by the following equation:

`y(t) = 46000(1.06)^(t)`

How many years will pass until the population of Frisco ISD is at 100,000 students?

This is t for which
`y(t) = 100000`. So

`y(t) = 46000(1.06)^(t)`

`46000(1.06)^(t) = 100000`

`(1.06)^(t) = (100000)/(46000)`

`\log{(1.06)^(t)} = \log{(100000)/(46000)}`

`t\log{1.06} = \log{(100000)/(46000)}`

`t = \frac{\log{(100000)/(46000)}}{\log{1.06}}`

`t = 13.33`

So the answer is ≈ 13.33 years