Certainly! Let's break down the problem step-by-step to determine the values of \( A \), \( b \), and \( c \) for the given situation.
1. Initial Price (A):
In 1979, the price of electricity was \( \$0.05 \) per kilowatt-hour. So, \( A \) is 0.05.
2. Growth Rate (b):
The price increases at a rate of 2.05% annually. When dealing with percentages in the context of growth, we convert the percentage into its decimal form and add 1 to it. Therefore,
[tex]\[
b = 1 + \frac{2.05}{100} = 1 + 0.0205 = 1.0205
\][/tex]
3. Target Price (c):
The target price we want to reach is \( \$0.10 \) per kilowatt-hour. So, \( c \) is 0.10.
Thus, the equation to determine how many years it will take for the price per kilowatt-hour to reach \( \$0.10 \) can be represented as:
[tex]\[
c = A(b)^t
\][/tex]
Substituting the values we have:
[tex]\[
0.10 = 0.05 (1.0205)^t
\][/tex]
So, the values of \( A \), \( b \), and \( c \) for this situation are:
[tex]\[
A = 0.05, \quad b = 1.0205, \quad c = 0.10
\][/tex]
