MATH SOLVE

6 months ago

Q:
# 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.

Accepted Solution

A:

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