Did you know?
Did you know that the function f(n)=2^n represents exponential growth, where the base 2 is raised to the power of n? This means that when n is increased, the output of the function grows exponentially. For example, when n is 5, the output (f(5)) would be 2^5, which equals 32.
Similarly, the function f(n)=5^n represents exponential growth as well, but with a base of 5. When n is increased, the output grows rapidly. For instance, when n is 4, the output (f(4)) would be 5^4, which equals 625.
Now, things get interesting with the function f(n)=(-2)^n. This function represents a combination of exponential growth and oscillation. The negative sign in front of the base (-2) indicates that the output alternates between positive and negative values. For instance, when n is 3, the output (f(3)) would be (-2)^3, which equals -8.
Lastly, the function f(n)=-2^n represents exponential decay, where the base (-2) is raised to the power of n. In this case, as n is increased, the output decreases exponentially. When n is 3, the output (f(3)) would be -2^3, which equals -8.
By understanding these concepts, you can make sense of the outputs for different values of n. Remember, exponential functions can depict both growth and decay, depending on the base and exponent used.
