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In 1979, the price of electricity was \[tex]$0.05 per kilowatt-hour. The price of electricity has increased at a rate of approximately 2.05% annually. If [tex]t[/tex] 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 \$[/tex]0.10. Fill in the values of [tex]A[/tex], [tex]b[/tex], and [tex]c[/tex] for this situation. Do not include dollar signs in the response.

[tex]c = A(b)^t[/tex]


Sagot :

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]