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:$$0.1 = 0.05(1.025)^t$$The values are: A = 0.05, b = 1.025, c = 0.1.What is an exponential function?An increasing exponential function is modeled by:$$A(t) = A(0)(1 + r)^t$$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 $$A(0) = 0.05$$The price of electricity has increased at a rate of approximately 2.05% annually, hence $$r = 0.025$$.Then, the equation is:$$A(t) = A(0)(1 + r)^t$$$$A(t) = 0.05(1 + 0.025)^t$$$$A(t) = 0.05(1.025)^t$$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:$$0.1 = 0.05(1.025)^t$$The values are: A = 0.05, b = 1.025, c = 0.1.You can learn more about exponential equations at