Next Week 1 Post Test 15 Type the correct answer in the box. In 1979, the price of electricity was $0.05 per kilowatt-hour. The price of electricity has increased at a rate of approximately 2.05% annually. If [tex]$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 $0.10. Fill in the values of [tex]$A, b$[/tex], and [tex]$c$[/tex] for this situation. Do not include dollar signs in the response. [tex]$c=A(b)^t$[/tex]
Answer (2)
Identify the initial price: A = 0.05 .
Calculate the annual growth factor: b = 1 + 0.0205 = 1.0205 .
Identify the target price: c = 0.10 .
The values are A = 0.05 , b = 1.0205 , and c = 0.10 .
Explanation
Understanding the Problem We are given the equation c = A ( b ) t , where:
A is the initial price of electricity in 1979.
b is the annual growth factor.
t is the number of years after 1979.
c is the target price of electricity.
We need to find the values of A , b , and c based on the information provided in the problem.
Finding A The initial price of electricity in 1979 was A = $0.05 per kilowatt-hour.
Finding b The price of electricity has increased at a rate of approximately 2.05% annually. Therefore, the annual growth factor is b = 1 + 0.0205 = 1.0205 .
Finding c The target price is c = $0.10 per kilowatt-hour.
Final Answer Therefore, the values are: A = 0.05 b = 1.0205 c = 0.10
Examples
Exponential growth, like the increasing price of electricity, can be used to model many real-world phenomena. For example, it can help predict population growth, the spread of a virus, or the accumulation of interest in a bank account. Understanding exponential growth allows us to make informed decisions about the future, whether it's planning for resource allocation, managing public health crises, or making sound financial investments. The formula c = A ( b ) t is a fundamental tool in these analyses.
To find the values for the equation c = A ( b ) t , we have A = 0.05 , b = 1.0205 , and c = 0.10 . This setup allows us to determine when the price of electricity will reach $0.10 per kilowatt-hour. The equation to use is 0.10 = 0.05 ( 1.0205 ) t .
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