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A college with a graduating class of 4000 students in the year 2008 predicts that its graduating class
will grow 5% per year. Write an exponential function to model the number of students y in the graduating class t years
after 2008.

Respuesta :

Poltergeist

Answer:

[tex]y=4000*(1.05)^t[/tex]

Step-by-step explanation:

The graduating class grows by 5% each year, this means after 1 year the number of students graduating will be 105% of 4000, or

[tex]4000*\frac{105}{100} =4000*1.05[/tex]

And after 2 years it will be

[tex](4000*1.05)*1.05[/tex]

and so on. Thus, after [tex]t[/tex] years the number of students [tex]y[/tex] will be

[tex]\boxed{ y=400*(1.05)^t}[/tex]

abidemiokin

An exponential function to model the number of students y in the graduating class t years  after 2008 is y = 4000(1.05)^t

Exponential functions

The standard exponential function is expressed as:

y = ab^x

  • a is the initial population
  • b is the rate
  • x is the time

If a college with a graduating class of 4000 students in the year 2008 predicts that its graduating class  will grow 5% per year, hence the required exponential equation will be:

y = 4000(1.05)^t

Learn more on exponential function here: https://brainly.com/question/12940982

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