Question10 Lab Homework
Parnela Ngeng
09/05/24 1:27 PM
Question 20, 4.5.C6
HW Score: of 35 points
Points: 0 of 1
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For the scatter plot given to the right, determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data.
Choose the correct answer below.
A. a logarithmic function
B. an exponential function
C. a linear function
Studdy Solution
STEP 1
1. The scatter plot provided shows data points that appear to have a specific pattern.
2. The task is to determine the best model for the data: linear, exponential, or logarithmic.
3. A linear model implies a constant rate of change.
4. An exponential model implies a rate of change proportional to the current value.
5. A logarithmic model implies a rate of change that decreases over time.
STEP 2
1. Analyze the scatter plot visually.
2. Determine the pattern of the data points.
3. Compare the potential models (linear, exponential, logarithmic).
4. Select the best-fitting model based on the pattern observed.
STEP 3
Analyze the scatter plot visually.
Observe the distribution and alignment of the data points on the scatter plot.
STEP 4
Determine the pattern of the data points.
Based on the visual inspection, identify whether the data points align in a straight line, curve upwards, or curve downwards.
STEP 5
Compare the potential models.
1. **Linear**: Look for a straight-line pattern where the data points have a constant rate of change.
2. **Exponential**: Look for a pattern where the data points curve upwards (rapid increase) or downwards (rapid decrease).
3. **Logarithmic**: Look for a pattern where the rate of change decreases over time, typically starting steep and leveling off.
STEP 6
Select the best-fitting model based on the pattern observed.
Based on the observation in Step 2, choose the most appropriate function:
- If the points form a straight line, choose a linear function.
- If the points form a curve that increases or decreases rapidly, choose an exponential function.
- If the points form a curve that starts steep and levels off, choose a logarithmic function.
Given that the points appear to be roughly aligned in a straight line, the best choice is:
C. a linear function.
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