Question

1. consider the curve $y = 5(2^x)$. 13a determine the $y$-intercept of the exponential curve. $y = $ enter your next step here

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a curve is the point where the curve intersects the y - axis. At the y - axis, the value of \(x = 0\). So we need to substitute \(x=0\) into the equation \(y = 5(2^{x})\).

Step2: Substitute \(x = 0\) into the equation

Substitute \(x = 0\) into \(y=5(2^{x})\). We know that for any non - zero number \(a\), \(a^{0}=1\). So when \(x = 0\), \(2^{0}=1\). Then \(y=5\times(2^{0})=5\times1\).

Step3: Calculate the value of y

\(5\times1 = 5\).

Answer:

\(5\)