The population of a school will increase by 3% per year. In 2005, the population was 127 students. Use a graph to find when the population will be
Enter the correct year in the box.
Answers
Using an exponential function, it is found that the population will be of 350 students in the year of 2039, 34.3 years after 2005.
What is an exponential function?An increasing exponential function is modeled according to the rule presented as follows:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which the parameters of the equation is defined as follows:
A(0) is the initial amount of the function.r is the growth rate of the function, as a decimal.In the context of this problem, the values of the parameters are given as follows:
A(0) = 127, which is the number of students in the reference year of 2005.r = 0.03, which is the yearly increase rate.Hence the equation for the number of students in t years after 2005 is given as follows:
[tex]A(t) = 127(1.03)^t[/tex]
The number will be of 350 students when A(t) = 350, hence:
[tex]A(t) = 127(1.03)^t[/tex]
[tex]350 = 127(1.03)^t[/tex]
[tex](1.03)^t = \frac{350}{127}[/tex]
[tex]\log{(1.03)^t} = \log{\left(\frac{350}{127}\right)}[/tex]
[tex]t\log{1.03} = \log{\left(\frac{350}{127}\right)}[/tex]
[tex]t = \frac{\log{\left(\frac{350}{127}\right)}}{\log{1.03}}[/tex]
t = 34.3 years.
34.3 years = during the year of 2005 + 34.3 = 2039. This result is shown by the graph at the end of the answer.
Missing InformationThe problem asks for when the population will be of 350 students.
More can be learned about exponential functions at https://brainly.com/question/25537936
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
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Step-by-step explanation:
Important points to note:
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- 3 miles west of Seiling, the limestone layer was found at a depth of 270ft.
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