In the study of ecosystems, predator-prey models are often used to study the interaction between species. consider populations of tundra wolves, given by w(t), and caribou, given by c(t), in northern canada. the interaction has been modeled by the equations dc dt = ac − bcw dw dt = −cw + dcw. (a) what values of dc/dt and dw/dt correspond to stable populations?

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the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).