Graph y=2.4^x

Problem

y=2.4^x

Solution

1. Identify the type of function. This is an exponential growth function of the form y=a⋅b^x where a=1 and the base b=2.4 Since b>1 the graph will rise from left to right.

2. Determine the y-intercept. Set x=0 to find the point where the graph crosses the y-axis.

y=2.4^0=1

The y-intercept is (0,1)

3. Calculate additional points to define the curve.
   For x=1

y=2.4^1=2.4

For x=2

y=2.4^2=5.76

For x=−1

y=2.4^(−1)=1/2.4≈0.417

4. Identify the horizontal asymptote. As x approaches negative infinity, 2.4^x approaches 0
   The horizontal asymptote is the line y=0

5. Sketch the graph. Plot the points (−1,0.417) (0,1) (1,2.4) and (2,5.76) Draw a smooth curve through these points that stays above the x-axis and increases rapidly to the right.

Final Answer

y=2.4^x

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