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

Answer 1

To model the scenario described, where the average time it takes for Charles to get to work increases by approximately 2% per year starting from 24 minutes in 2012, we can use an exponential growth model.

The general form of an exponential growth equation is:

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

where:
- \( m \) is the amount after \( x \) years,
- \( a \) is the initial amount (24 minutes),
- \( r \) is the growth rate (in decimal form, so 2% is 0.02),
- \( x \) is the number of years.

In this case, the equation becomes:

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

So, the correct model for the number of minutes, \( m \), that it takes him to get to work if \( x \) represents the number of years since 2012 is:

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

This corresponds to the answer:

**m = 24(1.02)^x (m is equal to 24 times 1 point 0 2 to the x th power)**.