In the year 1930, the number of cartons of milk produced in the city of Dillus each year was 385,000. Each year since 1930, the number of cartons produced has increased on average by 4.75% over the amount produced by the previous year.

Question

Which function models the total number of cartons produced in x years since 1930?

Responses
A	m(x) = 385,000(1.475)xm ( x ) = 385,000(1.475) x
B	m(x) = 385,000(1.0475)xm ( x ) = 385,000(1.0475) x
C	m(x) = 385,000(0.9525)xm ( x ) = 385,000(0.9525) x
D	m(x) = 385,000(0.525)x

GPT-4o mini · Answer

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 $m (x) = 385, 000 (1.0475)^{x}$