SAT Saturday Week 16: Advanced Math & Exponential Functions

August 15, 2026

SAT Saturday: Advanced Math & Exponential Models

Student working on standardized test grid. — Image by Rafael Oliveira via Unsplash

Welcome to Week #16 of SAT Saturday! Approximately 35% of the SAT Math section focuses on Advanced Math. This category tests your mastery of complex equations, quadratics, exponential growth and decay, polynomials, and function notation. Today, we are reviewing last week’s linear algebra and rate-of-change solutions, then diving into custom operations and exponential word problems!

📝 Week #16 Practice Questions: Advanced Math & Exponents

Question 31: Complex Exponents & Custom Operations

If a new mathematical operation is defined as: $Unique math operation graphic: a (star) b = a ^ (2 + b)$ Evaluate :

A) 1
B) 100
C) 1/100
D) Undefined
E) 0

Question 32: Exponential Growth Functions (Grid-In Style)

Writing Equations from Context:

An investor deposits $2,500 into a high-yield savings account that earns 6% interest compounded annually. The value of the account after t years can be modeled by the function:

where c and x are constants. What is the value of x?

(Write down your answers! Full step-by-step solutions will be revealed in next week’s SAT Saturday post.)

💡 Quick SAT Math Tip for Week #16

The Exponential Growth & Decay Blueprint:

For any exponential model:

c (Initial Value): The starting amount at time t = 0.
x (Growth/Decay Factor):
- For Growth: x = (1 + rate)
- For Decay: x = (1 – rate)
Example: A 6% growth rate means x = 1 + 0.06 = 1.06.

🏆 Week #15 Answer Key & Detailed Explanations

Let’s review the step-by-step solutions for last week’s Algebra and Linear Functions questions.

Question 29: Interpreting Linear Constants

A logistics company uses the equation C = 2.50x + 75 to calculate the total cost, C, in dollars, for a ground delivery shipment traveling x miles. Which statement is the best interpretation of the number 75 in this context?

A) The cost increase, in dollars, for each additional mile traveled.
B) The total number of miles the delivery truck can travel on a single trip.
C) The minimum or initial charge, in dollars, to set up and load the shipment.
D) The average speed of the delivery truck in miles per hour.

Correct Answer: C) The minimum or initial charge, in dollars, to set up and load the shipment.

The Concept:

In linear equations of the form y = mx + b, the constant term b is the y-intercept.

The Breakdown:

The variable x represents the number of miles traveled.
Setting x = 0 gives C = 2.50(0) + 75 = 75.
Therefore, $75 represents the base charge before any distance is covered — the fixed setup or loading cost.

Question 30: Calculating Rates of Change from Graphs

Graph for question 30 with points (0, 60) and (5, 0) easily identifiable. The x-axis is marked as hours and the y-axis is marked as Thousands of gallons of waters.

Scenario:
A municipal maintenance crew is completely draining a commercial swimming pool to perform structural repairs. The graph above models the volume of water, V, in thousands of gallons, remaining in the pool t hours after the drainage pump is turned on.

Question:
Based on the graph, at what constant rate, in thousands of gallons per hour, is the water being drained from the swimming pool?

A) 10
B) 12
C) 50
D) 60

Correct Answer: B) 12

Step-by-Step Breakdown:

Identify the Goal: The phrase “at what constant rate… is the water being drained” tells us to find the rate of change (the magnitude of the slope).
Identify Two Grid Points:
- Point 1 (y-intercept): (60, 0) — The pool initially holds 60 thousand gallons.
- Point 2 (x-intercept): (5, 0) — The pool is empty after 5 hours.
Calculate the Slope (m):
Interpret the Result: A slope of means the volume decreases by 12 thousand gallons per hour. The rate of drainage is 12 thousand gallons per hour (Option B).

⚠️ Trap Answer Breakdown:

Option A (10): A common calculation error caused by misreading axis grid lines.
Option C (50): Uses an arbitrary number that does not match key intercepts.
Option D (60): Identifies the initial volume of the pool (60 thousand gallons), not the rate of drainage.

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SAT Saturday Week 16: Advanced Math & Exponential Functions