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)x
m is equal to 1 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
m is equal to 24 times 1 point 0 2 to the x th power

m=0.02(24)x

Answer 1

The correct equation that models the number of minutes, \( m \), that it takes Charles to get to work, given that the average time increases by approximately 2% per year starting from an average of 24 minutes in 2012, is:

\[
m = 24(1.02)^x
\]

Here's the reasoning:

- The initial amount of time it takes (when \( x = 0 \), which is in 2012) is 24 minutes.
- Since the time is increasing by 2% per year, you multiply the previous year's time by \( 1.02 \) each year.

Thus, the model correctly reflects the growth in travel time over the years.