ESTION THREE Find the co-ordinates of the \( y \)-axis intercept for the exponential graph \( y=5^{3 x+2}+4 \) .

To find the \( y \)-axis intercept of the exponential graph \( y = 5^{3x + 2} + 4 \), we need to evaluate the function at \( x = 0 \). Substituting \( x = 0 \) into the equation gives: \[ y = 5^{3(0) + 2} + 4 = 5^2 + 4 = 25 + 4 = 29. \] Thus, the coordinates of the \( y \)-axis intercept are \( (0, 29) \). Now, a fun fact is that exponential functions like this one grow very rapidly! For small values of \( x \), you might still get manageable numbers, but as \( x \) increases, the output just skyrockets upwards. So even a tiny change in \( x \) for large values can lead to surprisingly high values of \( y \)! Additionally, exponential functions are widely used in real-world scenarios. They're fundamental in fields like finance for calculating compound interest, where investments grow exponentially over time. Understanding these growth patterns can help you make better financial decisions, especially in terms of savings and investments!