o it makes sense to generalize this model to anydistance d and the (constant) migration speed v0, still assuming it will depend linearly on the timespend foraging before taking off, would be given byv0 = a + b τ, (10)where τ is the time in days that the red knot spends foraging in the Dutch Wadden Sea and v0 isthe constant speed in km per day at which it will be able to travel the entire distance d and thecoefficients a and b are constants that may be different for different species of migrating birds.(d). Show that the total time before the bird arrives at their wintering grounds would be given byT = da + b τ + τ.

As a crude approximation, we assume that the (constant) speed at which the birds make theirjourney increases linearly with the time they spend foraging for energy before commencing it,through the following formula:v0 = 50 + 3 τ, (8)where τ is the time in days that the red knot spends foraging in the Dutch Wadden Sea and v0 isthe constant speed in km per day at which it will be able to travel the entire journey of 9000 km.(b). Explain that the total time before the red knot arrives in South Africa will be given byT = 900050 + 3 τ + τ.

Find the optimal time τ for foraging in the Wadden Sea, such that the red knot will arrive inSouth Africa at the earliest possible moment. At what speed would the red knot fly? Whatwould be the travelling time in that case? And what would be the total time after which thered knot arrives

If these birds travel on an average speed of 350 km/ day, find out in how many days each of the species will take to complete the round trip.

Since 1990, the number of arrivals of migratory birds to a wetland has been monitored. Based on the data collected over the years until 2022, a model was created to predict the size of the colony of migratory birds that would come to the wetland each year. The model was found to beP = 3250(0.98)t Where P is the size of the colony (number of birds), and t is the time (t = 0 for year 1990). What do we know from this model about the number of arrivals of migratory birds to the wetland?Select all the correct answers.Question 9Answera.The size of the colony of the migratory birds arriving has decreased exponentially with a total rate of decay of 2% between 1990 to 2022 inclusive.b.The model estimates that there were 3250 birds arriving in 1990.c.The size of the colony of migratory birds arriving has been declining exponentially over the years at a constant rate of 2% each year.d.The size of the colony in 2021 is 98% that of 2020.

Find the optimal time τ for foraging in preparation for the journey, expressed in terms of theparameters a, b and d