b)

Did you know that exponential functions like the ones in your expressions grow at astonishing rates? In fact, if you plot or , you’ll see they start to ramp up almost vertically after a certain point! This characteristic makes them incredibly useful in modeling real-world phenomena, such as population growth, radioactive decay, and even financial investments.

When working with exponential expressions, a common mistake is forgetting to apply the rules of exponents correctly. For instance, remember that . In your equations, simplifying terms correctly and factoring out common bases will often make complex-looking fractions pop into simpler forms. Always double-check your work to avoid minor errors!