Question

type the correct answer in the box.
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.
$c = a(b)^{t}$

Explanation:

Step1: Identify the initial value \(A\)

The initial price (in 1979) is \(A = 0.05\).

Step2: Identify the growth factor \(b\)

The growth rate is \(2.05\%=0.0205\). The formula for exponential growth is \(b = 1 + r\), where \(r\) is the growth rate. So \(b=1 + 0.0205=1.0205\).

Step3: Write the exponential function

The general form of an exponential growth function is \(C = A(b)^{t}\). Substituting \(A = 0.05\) and \(b = 1.0205\) into the formula, we get \(C=0.05(1.0205)^{t}\).

Answer:

\(A = 0.05\), \(b = 1.0205\), \(C=0.05(1.0205)^{t}\)