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In 1979, the price of electricity was $0.05 per kilowatt-hour. The price of electricity has increased at a rate of approximately 2.05% annually. If t is the number of years after 1979, create the equation that can be used to determine how many years it will take for the price per kilowatt-hour to reach $0.10. Fill in the values of A, b, and c for this situation. Do not include dollar signs in the response.

c = A(b)^t

Respuesta :

The exponential equation that can can be used to determine how many years it will take for the price per kilowatt-hour to reach $0.10 is:

[tex]0.1 = 0.05(1.025)^t[/tex]

  • The values are: A = 0.05, b = 1.025, c = 0.1.

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the growth rate, as a decimal.

In this problem:

  • In 1979, the price of electricity was $0.05 per kilowatt-hour, hence [tex]A(0) = 0.05[/tex]
  • The price of electricity has increased at a rate of approximately 2.05% annually, hence [tex]r = 0.025[/tex].

Then, the equation is:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 0.05(1 + 0.025)^t[/tex]

[tex]A(t) = 0.05(1.025)^t[/tex]

The time in years it will take for the price per kilowatt-hour to reach $0.10 is t for which A(t) = 0.1, hence:

[tex]0.1 = 0.05(1.025)^t[/tex]

  • The values are: A = 0.05, b = 1.025, c = 0.1.

You can learn more about exponential equations at https://brainly.com/question/25537936

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