Question

There were 800 farmers' markets initially in the usa in 2012. in 2013, the number of farmers' markets was 1.25 times the initial number of farmers' markets. then, in 2014, the number of farmers' markets was 1.25 times the number of farmers' markets the previous year. if this pattern continues, which of the following graphs represents the number of farmers' markets in the usa over time? a. graph w b. graph x c. graph y d. graph z

Answer 1

The graph representing the number of farmers' markets that increases by 1.25 times each year would be exponential growth because the increase is multiplicative. Therefore, we are looking for a graph that shows a consistently steepening curve over time.

Step-by-step explanation:

The question is about calculating the number of farmers' markets in the USA over a period of time when there is a steady yearly increase by a multiplier. To solve this, we can use the concept of geometric progression, as each year the number increases by a factor of 1.25 times the previous year's number.

Starting with 800 farmers' markets in 2012, for 2013 we multiply 800 by 1.25 to get 1000 farmers' markets. For 2014, we again multiply the previous year's number (1000) by 1.25 to find the next value in the sequence, which would be 1250 farmers' markets. This pattern will continue each year, representing a geometric growth.

Given this information, the correct graph representing the number of farmer's markets over time would show a consistent increasing curve, getting steeper with time. Assuming the choices provided in the graphs are typical line graphs, the correct graph would be exponential growth and not linear, as the increase is multiplicative rather than additive.

Answer 2

The correct answer is Graph Z.

Here's why:

In 2012, there were 800 farmers' markets.

In 2013, the number of farmers' markets increased by 25%, as 1.25 times 800 is 1000.

In 2014, the number of farmers' markets increased by another 25%, as 1.25 times 1000 is 1250.

Graph Z shows this pattern correctly. It starts at 800 in 2012 and increases by 25% each year. The other graphs do not match this pattern:

Graph W starts at 800 and increases linearly, which is not what the question describes.

Graph X starts at 800 and increases exponentially, which is also not what the question describes.

Graph Y starts at 0 and increases linearly, which is not what the question describes and is not possible in this context.

Therefore, based on the information provided in the question and the pattern of increasing by 25% each year, Graph Z is the only graph that correctly represents the number of farmers' markets in the USA over time.

Complete the image: