The values of P₀ and k of the given function are;
P₀ = 194 and k = -1.609
Decay Functions
We are given the function; P = 194(0.2)^(t)
We want to put that function in the form P = P₀e^(kt)
We know that e has a value of approximately 2.7183
Thus, our second equation will be;
P = P₀*2.7183^(kt) ----(3)
Put P₀*2.7183^(kt) for P in the first equation to get;
P₀*2.7183^(kt) = 194(0.2)^(t)
This means that; P₀ = 194
Now, let us divide the third eq by the first equation to get;
1 = ((0.2)^(t))/(2.7183^(kt))
2.7183^(kt) = (0.2)^(t)
kt In 2.7183 = t In 0.2
kt = -1.609t
k = -1.609
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