To model the total number of cartons of milk produced in \( x \) years since 1930, we need to consider that the production increases by 4.75% each year. This means that each year, the production multiplies by \( 1 + 0.0475 = 1.0475 \).
The general formula for exponential growth can be described as:
\[ m(x) = m_0 \cdot r^x \]
where:
- \( m_0 \) is the initial amount (the amount produced in 1930),
- \( r \) is the growth factor,
- \( x \) is the number of years since 1930.
Given:
- \( m_0 = 385,000 \)
- \( r = 1.0475 \)
The function modeling the total number of cartons produced \( x \) years since 1930 is:
\[ m(x) = 385,000 \cdot (1.0475)^x \]
Based on the options provided, the correct response is:
B \( m(x) = 385,000(1.0475)^x \)