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Charles tracked the average amount of time that it takes for him to get to work and he found that it has been increasing by app...Question
Charles tracked the average amount of time that it takes for him to get to work and he found that it has been increasing by approximately 2% per year over the past several years. When he started tracking this in the year 2012, it took him an average of 24 minutes to get to work. Which equation best models the number of minutes, m, that it takes him to get to work if x represents the number of years since 2012?(1 point) Responses m=1.02(24)xm=1.02(24)xm is equal to 1 point 0 2 times 24 to the x th power m=0.02(24)xm=0.02(24)xm is equal to 0 point 0 2 times 24 to the x th power m=(0.02)xm=(0.02)xm is equal to 0 point 0 2 to the x th power m=24(1.02)x
Answers
GPT-4o mini
To model the average time it takes Charles to get to work, we can use the formula for exponential growth. Since the time increases by approximately 2% per year, we can express this as follows:
1. The initial time it took him to get to work in 2012 is 24 minutes.
2. The growth factor for a 2% increase is 1.02.
Therefore, the equation that models the number of minutes \( m \) as a function of \( x \) (the number of years since 2012) is:
\[ m = 24(1.02)^x \]
So the correct answer is:
**m = 24(1.02)^x**
1. The initial time it took him to get to work in 2012 is 24 minutes.
2. The growth factor for a 2% increase is 1.02.
Therefore, the equation that models the number of minutes \( m \) as a function of \( x \) (the number of years since 2012) is:
\[ m = 24(1.02)^x \]
So the correct answer is:
**m = 24(1.02)^x**