Question

2 the graph shows the amount of a chemical in a water sample. it is decreasing exponentially.
find the coordinates of the points labeled a, b and c.
explain your reasoning.
3 the graph shows the amount of a chemical in a water sample at different times after it was first measured.
select all statements that are true.
a the amount of the chemical in the water sample appears to be decreasing exponentially.
b the amount of the chemical in the water sample appears to be increasing exponentially.
c the amount of the chemical in the water sample appears to be changing linearly.
d when it was first measured, there were 2,000 mg of the chemical in the water sample
e after 4 hours, there were 100 mg of the chemical in the water.

Explanation:

First Problem (Finding Coordinates of A, B, C)

1. For point A: Match its position to the x-axis (time) value of 2, and the y-axis (chemical amount) value of 700, since it follows the exponential decay pattern of the given points (0,1000), (1,800) with consistent decreasing intervals.
2. For point B: Match its position to the x-axis value of 3, and the y-axis value of 600, continuing the exponential decay trend.
3. For point C: Match its position to the x-axis value of 4, and the y-axis value of 500, following the observed decay pattern.

• Option A: The data points show a rapid initial decrease that slows over time, which matches the shape of an exponential decay curve.
• Option B: The amount of chemical clearly decreases, not increases, so this is false.
• Option C: A linear change would show equal decreases per hour, but the decreases get smaller (2000→1000 is -1000, 1000→700 is -300), so this is false.
• Option D: At x=0 (first measurement), the y-value is 2000 mg, so this is true.
• Option E: At x=4 hours, the y-value is 400 mg, not 100 mg, so this is false.

Answer:

• Point A: (2, 700)
• Point B: (3, 600)
• Point C: (4, 500)

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Second Problem (Select True Statements)