题目
题目
多项填空题

Question textGuidelines to answer the following question:Fill in the blanks with the correct answers. Do NOT use any spaces or brackets.For all numerical answers, give EXACT values (i.e. do not round your answers) unless instructed otherwise in the question.If using fractions, give answers as SIMPLIFIED fractions using the forward slash (e.g. 1/2 or 5/4).Use - for any negatives.______________________________________________________________________________________________This question is worth 1 + 1 + 1 + 2 = 5 marks.The population of rabbits on a particular island, [math: t] weeks after a virus is introduced is modelled by[math: P=1800e−0.05t]P=1800e^{-0.05t}, where [math: P] is the number of rabbits.a. Find the initial size of the population.[math: t=] Answer 1 Question 6[input] weeks[math: P=] Answer 2 Question 6[input] rabbits [1 mark]b. Find the time taken for the initial population to halve. Express your answer to the nearest week.[math: P=] Answer 3 Question 6[input] rabbits[math: t=] Answer 4 Question 6[input] weeks [1 mark]After 18 weeks, the virus has become ineffective and the population of rabbits, [math: PN]P_{N} , starts to increase again according to the new model [math: PN=732+2(t−18)loge(2t−35)]P_{N}=732+2(t-18)log_{e}(2t-35), where [math: t] is the number of weeks since the virus was first introduced.c. State the domain of [math: PN]P_{N}.[math: t] Answer 5 Question 6[select: , greater than, less than or equal to, greater than or equal to, less than] Answer 6 Question 6[input] weeks [1 mark]d. Find the size of the population after 30 weeks. Give your answer to the nearest whole number.[math: PN=]P_{N}= Answer 7 Question 6[input] [math: +2(]+2 ( Answer 8 Question 6[input] [math: )loge(])\:log_e\:( Answer 9 Question 6[input][math: )]Population [math: =] Answer 10 Question 6[input] rabbits ( to nearest whole number) [2 marks]

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The problem presents a sequence of fill-in-the-blank items based on two models for rabbit population and asks for exact numerical values without spaces or brackets. I’ll walk through each part step by step, showing how to determine the required quantities and interpreting the given models. a. Initial size of the population - The model for population P as a function of time t (in weeks) is P = 1800 e^(−0.05 t). - The initial population corresponds to t = 0 weeks. Substitute t = 0 into the formula: P = 1800 e^(−0.05 ......Login to view full explanation

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