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?
A. m = (0.02)^x
B. m = 24(1.02)^x
C. m = 0.02(24)
D. m = 1.02(24)^x

Answer 1

To model the situation presented, we need an equation that represents the average commute time increasing by 2% each year starting from an initial time of 24 minutes in 2012. The general form for exponential growth is:

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

where:
- \( m_0 \) is the initial amount (in this case, 24 minutes),
- \( r \) is the growth rate (in this case, 0.02 for 2%),
- \( x \) is the number of years since the starting year (2012).

Substituting the values into the equation, we have:

\[ m = 24 \cdot (1 + 0.02)^x \]
\[ m = 24 \cdot (1.02)^x \]

Thus, the equation that best models the number of minutes, \( m \), that it takes Charles to get to work after \( x \) years since 2012 is:

**B. \( m = 24(1.02)^x \)**