Answer: Choice C
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Step-by-step explanation:
An exponential function can be written in the form
y = a*b^x
where,
- a = y intercept
- b = tied to either growth or decay
If 0 < b < 1, then we have decay. If b > 1, then we have growth.
For choice A, we need to rewrite that negative exponent to make it positive. So we have
to show we have decay going on since b = 1/6. If it helps, then 1/6 = 0.167 approximately.
Similarly, choices B and D also show decay because those b values are between 0 and 1 excluding each endpoint.
Choice C on the other hand has b = 4/3 = 1.333 approximately to fit the inequality b > 1. Therefore, choice C represents exponential growth and not decay.
You can use graphing tools like a TI83, geogebra, or desmos to visually confirm that graph C is an exponential growth function that goes up forever as you move to the right.
The others move closer and closer to the x axis (but never reach it due to it being an asymptote), which show that we have decay for graphs A, B and D.