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 $0.10. Fill in the values of A, b, and c for this situation. Do not include dollar signs in the response.
[tex]c=A(b)^t[/tex]
Answer (1)
The initial price A in 1979 is 0.05 .
The growth factor b is calculated as 1 + 0.0205 = 1.0205 .
The target price c to be reached is 0.10 .
The values are A = 0.05 , b = 1.0205 , and c = 0.10 , so the equation is c = 0.10 , A = 0.05 , b = 1.0205 .
Explanation
Understanding the Equation We are given the equation c = A ( b ) t , where:
A is the initial price of electricity in 1979.
b is the growth factor, representing the annual increase in price.
t is the number of years after 1979.
c is the price per kilowatt-hour after t years.
We need to find the values of A , b , and c for this situation.
Finding A The initial price of electricity in 1979 was 0.05 p er ki l o w a tt − h o u r . T h ere f ore , A = 0.05$.
Finding b The price of electricity increases at a rate of 2.05% annually. To find the growth factor b , we add the percentage increase to 1: b = 1 + 0.0205 = 1.0205
Finding c We want to find the number of years it will take for the price per kilowatt-hour to reach 0.10. T h ere f ore , c = 0.10$.
Final Answer Now we have the values for A , b , and c :
A = 0.05
b = 1.0205
c = 0.10
So, the equation is 0.10 = 0.05 ( 1.0205 ) t .
Examples
Exponential growth models are incredibly useful in finance for calculating compound interest. For instance, if you invest 1 , 000 inana cco u n tt ha t e a r n s 5 t ye a rs w o u l d b e V = 1000(1.05)^t , w h ere V$ is the value of the investment. This model helps you project the future value of your investment and plan accordingly. Understanding exponential growth can also be applied to population growth, where you can predict future population sizes based on current growth rates.
