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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 that 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)x
m is equal to 1 point 0 2 times 24 to the x th power
m=0.02(24)x
m is equal to 0 point 0 2 times 24 to the x th power
m=(0.02)x
m is equal to 0 point 0 2 to the x th power
m=24(1.02)x
Which equation best models that 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)x
m is equal to 1 point 0 2 times 24 to the x th power
m=0.02(24)x
m is equal to 0 point 0 2 times 24 to the x th power
m=(0.02)x
m is equal to 0 point 0 2 to the x th power
m=24(1.02)x
Answers
GPT-4o mini
The correct equation that models the number of minutes, \( m \), that it takes Charles to get to work, given that the time increases by approximately 2% per year starting from 24 minutes in 2012, is:
\[ m = 24(1.02)^x \]
Here, \( 24 \) is the initial time it took to get to work, \( 1.02 \) represents the 2% increase (or 100% + 2%), and \( x \) is the number of years since 2012. Thus, as \( x \) increases, the equation shows the compounded growth in travel time.
\[ m = 24(1.02)^x \]
Here, \( 24 \) is the initial time it took to get to work, \( 1.02 \) represents the 2% increase (or 100% + 2%), and \( x \) is the number of years since 2012. Thus, as \( x \) increases, the equation shows the compounded growth in travel time.