Question

Select "Growth" or "Decay" to classify each function. Select "Growth" or "Decay" to classify each function. Function Growth Decay y=200(0.5)2t y=12(2.5)t6 y=(0.65)t4 Function Growth Decay y = 200 (0.5) 2t y = 12 (2.5) t6 y = (0.65) t4

Answer 1

Equations with a number in brackets that is less then one is a decaying function.
Y=200(0.5)2t Decay
Y=12(2.5)t6 Growth
Y=(0.65)t4 decay
Hope this helps!

Answer 2

The functions $y=200(0.5)^{2t},y=12(2.5)^{\frac{t}{6}}, \; \rm{and }\; \it{y}=\rm(0.65)^{\frac{\it t}{\rm4}}$ will be decay, growth, and decay functions, respectively.

The given functions are:

$y=200(0.5)^{2t}\\y=12(2.5)^{\frac{t}{6}}\\ y=(0.65)^{\frac{t}{4}}$

It is required to find the given functions are growth or decay functions.

Growth function is a function in which the value of the function increases with the increase in value of t. Decay function is a function in which the value of the function decreases with the increase in value of t.

So, the function $y=200(0.5)^{2t}$ is a decay function because 2t is in power of 0.5 (<1). The value of the function will decrease with increase in t.

Similarly, the function $y=(0.65)^{\frac{t}{4}}$ will be a decay function as t/4 is in power to a fraction 0.65.

Now, the function $y=12(2.5)^{\frac{t}{6}}$ will be a growth function because t/6 is in power of 2.5 (>1). The value of the function will increase with increase in t.

Therefore, the functions $y=200(0.5)^{2t},y=12(2.5)^{\frac{t}{6}}, \; \rm{and }\; \it{y}=\rm(0.65)^{\frac{\it t}{\rm4}}$ will be decay, growth, and decay functions, respectively.

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