this graph shows the populations of baltimore and cleveland in the 20th century. b(t) is the population of baltimore in year t. c(t) is the population of cleveland in year t.
a) estimate the b(1930) and explain what it means in this situation.
b) here are pairs of statements about the two populations. in each pair, which statement
explain how you know.
i) b(2000)>c(2000) or b(2000)<c(2000)
ii) b(1900)=c(1900) or b(1900) > c(1900)
c) were the two cities’ populations ever the same? if so, when?

Question

Accepted Answer

### Part (a)
# Explanation:
## Step1: Locate 1930 on x - axis
Find the year 1930 on the horizontal (x - axis) of the graph.
## Step2: Find B(1930) on the graph
Look at the line for Baltimore (B) at the year 1930. From the graph, we can see that at $t = 1930$, the population of Baltimore (the value of $B(1930)$) is approximately 800,000.
## Step3: Interpret the meaning
$B(1930)$ represents the population of Baltimore in the year 1930. So, it means that in 1930, the population of Baltimore was approximately 800,000 people.

# Answer:
$B(1930)\approx800000$. It means the population of Baltimore in 1930 was about 800,000.

### Part (b) (i)
# Explanation:
## Step1: Locate 2000 on x - axis
Find the year 2000 on the x - axis of the graph.
## Step2: Compare B(2000) and C(2000)
Look at the lines for Baltimore (B) and Cleveland (C) at the year 2000. The line for Baltimore (B) is above the line for Cleveland (C) at $t = 2000$. So, $B(2000)>C(2000)$.

# Answer:
$B(2000)>C(2000)$. We know this because at $t = 2000$, the graph of $B(t)$ (Baltimore's population) is above the graph of $C(t)$ (Cleveland's population).

### Part (b) (ii)
# Explanation:
## Step1: Locate 1900 on x - axis
Find the year 1900 on the x - axis of the graph.
## Step2: Compare B(1900) and C(1900)
Look at the lines for Baltimore (B) and Cleveland (C) at the year 1900. The line for Baltimore (B) is above the line for Cleveland (C) at $t=1900$. So, $B(1900)>C(1900)$.

# Answer:
$B(1900)>C(1900)$. We know this because at $t = 1900$, the graph of $B(t)$ (Baltimore's population) is above the graph of $C(t)$ (Cleveland's population).

### Part (c)
# Explanation:
## Step1: Check for intersection of graphs
We need to see if the two lines (representing $B(t)$ and $C(t)$) intersect at any point on the graph.
## Step2: Identify intersection years
From the graph, we can observe that the two lines (Baltimore's population line and Cleveland's population line) intersect at two points. One intersection point is around the year 1910 (when the two populations were equal) and another intersection point is around the year 1940 (when the two populations were equal again).

# Answer:
Yes, the two cities' populations were the same. This happened around the year 1910 and around the year 1940 (when the graphs of $B(t)$ and $C(t)$ intersect).

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Locate 1930 on x - axis

Step2: Find B(1930) on the graph

Step3: Interpret the meaning

Step1: Locate 2000 on x - axis

Step2: Compare B(2000) and C(2000)

Step1: Locate 1900 on x - axis

Step2: Compare B(1900) and C(1900)

Answer:

Part (b) (i)