Question

graph the following function.
$y = 5 \cdot 2^x$
show your work here
(there is a coordinate plane with a draw button above it)

Explanation:

Step1: Identify the function type

The function \( y = 5 \cdot 2^x \) is an exponential function of the form \( y = a \cdot b^x \), where \( a = 5 \) (the initial value) and \( b = 2 \) (the base, \( b>1 \), so it's an exponential growth function).

Step2: Find key points

• When \( x = 0 \): \( y = 5 \cdot 2^0 = 5 \cdot 1 = 5 \). So the point is \( (0, 5) \).
• When \( x = 1 \): \( y = 5 \cdot 2^1 = 5 \cdot 2 = 10 \). So the point is \( (1, 10) \).
• When \( x = -1 \): \( y = 5 \cdot 2^{-1} = 5 \cdot \frac{1}{2} = 2.5 \). So the point is \( (-1, 2.5) \).

Step3: Plot the points and draw the curve

Plot the points \( (0, 5) \), \( (1, 10) \), \( (-1, 2.5) \) on the coordinate plane. Since it's an exponential growth function (base \( 2>1 \)), the curve should pass through these points, increase as \( x \) increases, and approach the \( x \)-axis (but never touch it) as \( x \) decreases (since exponential functions with \( b>0, b
eq1 \) have a horizontal asymptote at \( y = 0 \) when \( a>0 \) and \( b>0 \), \( b
eq1 \)).

Answer:

To graph \( y = 5 \cdot 2^x \):

1. Plot key points: \( (0, 5) \), \( (1, 10) \), \( (-1, 2.5) \).
2. Draw a smooth curve through these points, showing exponential growth (increasing as \( x \) increases, approaching \( y = 0 \) as \( x \to -\infty \)).