Solving the Exponential Function y = 4(5)^n | Step-by-Step Guide and Examples

y = 4(5)ⁿ

The given equation is y = 4(5)ⁿ

The given equation is y = 4(5)ⁿ.

This equation represents an exponential function, where the base is 5, and the variable n is the exponent. Let’s break it down step by step:

1. The base of the exponential function is 5. This means that the value 5 is multiplied by itself n times.

2. The n represents the exponent. It determines how many times the base, which is 5 in this case, is multiplied by itself. The exponent can be any real number.

3. The coefficient 4 in front of the base means that the result of the exponential function is then multiplied by 4.

To better understand this equation, let’s substitute some values for n and calculate y:

– If n = 0, then y = 4(5)⁰. Since any number raised to the power of 0 equals 1, the equation simplifies to y = 4(1) = 4.

– If n = 1, then y = 4(5)¹. Since any number raised to the power of 1 remains the same, the equation simplifies to y = 4(5) = 20.

– If n = 2, then y = 4(5)². To calculate this, we need to evaluate 5² first, which means 5 multiplied by itself: y = 4(25) = 100.

Similarly, you can substitute different values for n to find the corresponding values of y.

In summary, the given equation y = 4(5)ⁿ represents an exponential function where the base, 5, is raised to the power of n and then multiplied by 4.

More Answers:
Understanding Exponentiation | Exploring the Power of a Math Operation a^x
Exploring Prime Numbers, Composite Numbers, Quadratic Equations, Differentiation, and Integration in Math
Understanding the Exponential Function | Properties and Applications of e^x

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