The population of a bird colony P(t) changes at a rate R(t) = e-0.5t dt (thousands...

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The population of a bird colony P(t) changes at a rate R(t) = e-0.5t dt (thousands of birds per year) for t years after settling. When the colony first arrived, there were eight thousand birds. (a) Determine how much the bird population will change between the first and second year after they settled. If applicable, please round the value to the nearest whole bird. (b) Explain the meaning of 8 + R(x) dx in context of this problem and find the value of the expression. If applicable, please round the value to the nearest whole bird. (c) Your buddy Ron draws a rough sketch of R(t) below. Sketch of R(t) --- --- -- --- He states "I'm sad that the population of birds is decreasing." Circle a response below and justify your selection. Ron might be correct Ron is definitely incorrect Ron is definitely correct The population of a bird colony P(t) changes at a rate R(t) = e-0.5t dt (thousands of birds per year) for t years after settling. When the colony first arrived, there were eight thousand birds. (a) Determine how much the bird population will change between the first and second year after they settled. If applicable, please round the value to the nearest whole bird. (b) Explain the meaning of 8 + R(x) dx in context of this problem and find the value of the expression. If applicable, please round the value to the nearest whole bird. (c) Your buddy Ron draws a rough sketch of R(t) below. Sketch of R(t) --- --- -- --- He states "I'm sad that the population of birds is decreasing." Circle a response below and justify your selection. Ron might be correct Ron is definitely incorrect Ron is definitely correct