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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

Respuesta :

Answer:

≈ 13.33 years

Step-by-step explanation:

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

[tex]y(t) = 46000(1.06)^{t}[/tex]

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

This is t for which [tex]y(t) = 100000[/tex]. So

[tex]y(t) = 46000(1.06)^{t}[/tex]

[tex]46000(1.06)^{t} = 100000[/tex]

[tex](1.06)^{t} = \frac{100000}{46000}[/tex]

[tex]\log{(1.06)^{t}} = \log{\frac{100000}{46000}}[/tex]

[tex]t\log{1.06} = \log{\frac{100000}{46000}}[/tex]

[tex]t = \frac{\log{\frac{100000}{46000}}}{\log{1.06}}[/tex]

[tex]t = 13.33[/tex]

So the answer is ≈ 13.33 years