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)xm=(0.02)xm is equal to 0 point 0 2 to the x th power m=24(1.02)xm=24(1.02)xm is equal to 24 times 1 point 0 2 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=1.02(24)x

Answer 1

To model the average time it takes Charles to get to work, we can use the concept of exponential growth since it is increasing by approximately 2% per year. Starting with the initial time it took him, 24 minutes, we can represent the increase each year using the formula for exponential growth:

\[ m = m_0(1 + r)^x \]

where:
- \( m_0 \) is the initial amount (initial time it took to get to work),
- \( r \) is the rate of increase (as a decimal),
- \( x \) is the number of years since 2012.

In this case:
- \( m_0 = 24 \) minutes,
- \( r = 0.02 \) (since 2% as a decimal is 0.02).

Thus, the equation becomes:

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

Looking at the responses you provided, the correct option is:

**m = 24(1.02)^x**

This correctly models the increase in time taken to get to work based on the given percentage growth rate.