Respuesta :
The equation would be
[tex]0.10=0.05(1+0.0205)^t[/tex]
and it would take 34.16 years.
0.10 is the amount we're trying to get; 0.05 is the initial value; and 0.0205 is the percent of increase, 2.05%, written as a decimal number.
To evaluate, we combine everything in parentheses:
[tex]0.10=0.05(1.0205)^t[/tex]
Divide both sides by 0.05:
[tex]\frac{0.10}{0.05}=\frac{0.05(1.0205)^t}{0.05} \\ \\2=1.0205^t[/tex]
We solve this using a logarithm:
[tex]\log_{1.0205}2=t \\ \\34.16=t[/tex]
[tex]0.10=0.05(1+0.0205)^t[/tex]
and it would take 34.16 years.
0.10 is the amount we're trying to get; 0.05 is the initial value; and 0.0205 is the percent of increase, 2.05%, written as a decimal number.
To evaluate, we combine everything in parentheses:
[tex]0.10=0.05(1.0205)^t[/tex]
Divide both sides by 0.05:
[tex]\frac{0.10}{0.05}=\frac{0.05(1.0205)^t}{0.05} \\ \\2=1.0205^t[/tex]
We solve this using a logarithm:
[tex]\log_{1.0205}2=t \\ \\34.16=t[/tex]
The equation that can be used to determine how many years it will take for the price per kilowatt-hour to reach $0.10 is [tex]\rm 0.10=0.05(1+0.0205)^t[/tex] and by solving this equation the value of 't' is 34.16.
Given :
- 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.
From the given data the equation to determine how many years it will take for the price per kilowatt-hour to reach $0.10 is obtained as:
[tex]\rm 0.10=0.05(1+0.0205)^t[/tex]
Now, divide the above equation by 0.05 from both sides.
[tex]\rm \dfrac{0.10}{0.05} = (1+0.0205)^t[/tex]
[tex]2=(1+0.0205)^t[/tex]
Now, take the log on both sides in the above equation.
[tex]\rm log2=t\;log(1.0205)[/tex]
Now, divide both sides by log(1.0205) in the above equation.
[tex]\rm log_{1.0205}2=t[/tex]
t = 34.16
For more information, refer to the link given below:
https://brainly.com/question/1957976
