Fill in both rows. Use fractions or decimals.
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| 2x | |||||
| (½)x |
One guided lesson · 60 minutes
Exponents → SAT Models
Every SAT problem appears before its helper questions. Read the original, solve the steps, then submit the final answer.
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01
15 minutes
Exponent Foundations
Goal: understand what the exponent controls, including zero and negative exponents.
Why is 2−3 equal to 1/8 rather than −8?
Complete the identity: (½)x = 2_____
Evaluate without a calculator.
02
10 minutes
Desmos Graph Lab
Your task
Graph three functions and compare them.
- Open Desmos.
- Enter
y=2^x,y=(1/2)^x, andy=2^(-x). - Click each graph at x = −2, −1, 0, 1, and 2.
- Use what you see to answer question 5.
Which two graphs overlap exactly?
03
30 minutes
Guided SAT Problems
Each block is one problem. The original SAT prompt comes first; the smaller questions underneath are steps toward its final answer.
Main SAT problem · the problem from the previous lesson
Problem A — Exponential decay
Then solve it in steps
The questions below unpack the same problem. They are not separate exercises.
Estimate the y-intercept. In y = a(b)x, approximately what is a?
The curve decreases as x increases. What must be true about b?
Which answer choice is closest to the value of b?
Main SAT problem · Question ID d6af3572
Problem B — Interpreting slope in context
Then solve it in steps
The questions below unpack the same problem. They are not separate exercises.
What the variables meanx = years since 1940y = minimum wage in dollars per hourModel: y = 0.096x − 0.488
What does an increase of 1 in x represent?
What is the slope of the model?
What does the line of best fit predict?
Main SAT problem · Question ID 2e8027b0
Problem C — Transforming a data set
Then solve it in steps
The questions below unpack the same problem. They are not separate exercises.
What changes?Every y-coordinate is multiplied by 3.9.Therefore both the y-intercept and the slope are multiplied by 3.9.
The original y-intercept is about 12. What is the new y-intercept?
The original slope is about 1.5. What is the new slope?
Which equation could be a line of best fit for data set F?
Main SAT problem · Question ID 1e1027a7
Problem D — Building a line of best fit
Then solve it in steps
The questions below unpack the same problem. They are not separate exercises.
What the variables meant = high temperature in °Cd = ice cream sales in dollarsUse two points on the drawn line, not two scatterplot dots.
Using about (12, 480) and (24, 880), estimate the slope.
Use d = 33t + b and the point (12, 480). Find b.
Which equation could represent the line of best fit?
04
5 minutes