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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=(0.02)x m is equal to 0 point 0 2 to the x th power m=24(1.02)x m is equal to 24 times 1 point 0 2 to the x th power 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
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GPT-4o mini
To model the situation where Charles's commute time increases by approximately 2% per year starting from 24 minutes in the year 2012, we can use the formula for exponential growth:
\[ m = m_0 (1 + r)^x \]
where:
- \( m_0 \) is the initial value (24 minutes),
- \( r \) is the rate of increase (0.02 for 2%),
- \( x \) is the number of years since 2012.
In this case, the equation becomes:
\[ m = 24 (1 + 0.02)^x \]
\[ m = 24 (1.02)^x \]
From the options provided, the equation that best represents this situation is:
**m = 24(1.02)^x**
Thus, the correct response is: **m = 24(1.02)^x.**
\[ m = m_0 (1 + r)^x \]
where:
- \( m_0 \) is the initial value (24 minutes),
- \( r \) is the rate of increase (0.02 for 2%),
- \( x \) is the number of years since 2012.
In this case, the equation becomes:
\[ m = 24 (1 + 0.02)^x \]
\[ m = 24 (1.02)^x \]
From the options provided, the equation that best represents this situation is:
**m = 24(1.02)^x**
Thus, the correct response is: **m = 24(1.02)^x.**