How to Determine Exponential Graph Characteristics

TLDR; The video discusses how to determine exponential graphs with different characteristics, such as the value of A and B in the equation y = ab^x.

💡 Exponential Functions and Equations

All graphs have equations in the form y = a * b^x, making them exponential functions.

A is the initial value with a function value when x is equal to zero. It's also the starting amount before exponential growth or decay starts.

B, when between 0 and 1, represents exponential decay, resulting in a decreasing graph from left to right.

If greater than 1, it indicates exponential growth, leading to an increasing graph from left to right.

📈 Determining the Largest Value of B

To determine the largest value of B, focus on the graphs representing exponential growth or increasing functions, which are the black, brown, and green graphs.

The graph that's increasing the fastest will have the largest value of B, as it's going uphill the fastest, which in this case, is the black function.

📉 Determining the Smallest Value of B

To find the smallest value of B, focus on the graphs representing exponential decay or decreasing functions, which are the red and blue graphs.

The graph that's decreasing the fastest will have the smallest value of B, which in this case, is the red graph.

🔢 Determining the Largest Value of A

The brown graph has the largest value of A, as it has a y-intercept of positive 2, while all the other graphs have a y-intercept of positive 1.