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=24(1.02)x m is equal to 24 times 1 point 0 2 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=1.02(24)x
Answers
GPT-4o mini
To model the average time it takes Charles to get to work over the years, we note that the time increases by 2% each year. This implies that the time can be modeled by an exponential growth function.
Given:
- The initial time in 2012 (when \( x = 0 \)) is 24 minutes.
- The growth rate is 2%, which can be expressed as multiplying by \( 1.02 \) (100% + 2% = 102% = 1.02).
The equation for the time \( m \) as a function of the number of years \( x \) since 2012 is given by:
\[
m = 24(1.02)^x
\]
Therefore, the correct answer is:
\[
m = 24(1.02)^x
\]
Given:
- The initial time in 2012 (when \( x = 0 \)) is 24 minutes.
- The growth rate is 2%, which can be expressed as multiplying by \( 1.02 \) (100% + 2% = 102% = 1.02).
The equation for the time \( m \) as a function of the number of years \( x \) since 2012 is given by:
\[
m = 24(1.02)^x
\]
Therefore, the correct answer is:
\[
m = 24(1.02)^x
\]