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Zielflug [23.3K]
3 years ago
10

Evaluate each expression using the values in the given table. x minus−3 minus−2 minus−1 0 1 2 3 ​f(x) minus−9 minus−7 minus−5 mi

nus−3 minus−1 1 3 ​g(x) 3 2 1 0 minus−1 minus−2 minus−3 ​(a) ​(fcircle◦​g)(negative 1−1​) ​ (b) ​(gcircle◦​f)(11​) ​ (c) ​(fcircle◦​f)(11​)
Mathematics
1 answer:
Ymorist [56]3 years ago
6 0
A) (f∘g)(-1) = f(g(-1)) = f(1) = -1
b) (g∘f)(1) = g(f(1)) = g(-1) = 1
c) (f∘f)(1) = f(f(1)) = f(-1) = -5
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\begin{array}{rcl}2000e^{0.05t} & = & 5000e^{0.02t}\\e^{0.05t} & = & 2.5e^{0.02t}\\0.05t & = & \ln2.5 + 0.02t\\0.05t & = & 0.9163 + 0.02t\\0.03t & = & 0.9163\\t& = & \dfrac{0.9163}{0.03}\\\\& = & \mathbf{30.54}\\\end{array}\\\text{The populations of species A and B will be the same in $\large \boxed{\textbf{30.54 yr}}$}

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