Giant pandas are a vulnerable species famous for their consumption of large amounts of bamboo. Suppose we track the female population of a group of pandas year-to-year, and classify the pandas into three categories: cubs, subadults and adults. Say that u1 (t) denotes the amount of cubs in year t, ug(t) denotes the amount of subadults in year t and uz(t) denotes the amount of adults in year t. Assume the following about the population of pandas: • Cubs remain cubs for only one year - they have a mortality rate of 15% and the rest become subadults; • Approximately 25% of subadults mature to adults each year, approximately 20% of subadults die year year, and the rest remain in this classification; • On average, adults give birth to 0.5 new cubs each year; • 95% of adults survive from one year to the next. We can model the change in class structure each year using the model, u(t + 1) = Aü(t) where u(t) u2 (t) | and A is u3 (t) Number Number Number Number Number Number Number Number Number
Giant pandas are a vulnerable species famous for their consumption of large amounts of bamboo. Suppose we track the female population of a group of pandas year-to-year, and classify the pandas into three categories: cubs, subadults and adults. Say that u1 (t) denotes the amount of cubs in year t, ug(t) denotes the amount of subadults in year t and uz(t) denotes the amount of adults in year t. Assume the following about the population of pandas: • Cubs remain cubs for only one year - they have a mortality rate of 15% and the rest become subadults; • Approximately 25% of subadults mature to adults each year, approximately 20% of subadults die year year, and the rest remain in this classification; • On average, adults give birth to 0.5 new cubs each year; • 95% of adults survive from one year to the next. We can model the change in class structure each year using the model, u(t + 1) = Aü(t) where u(t) u2 (t) | and A is u3 (t) Number Number Number Number Number Number Number Number Number
Advanced Engineering Mathematics
10th Edition
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Chapter2: Second-order Linear Odes
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![Giant pandas are a vulnerable species famous for their consumption of large amounts of bamboo. Suppose we track the female population of a group of
pandas year-to-year, and classify the pandas into three categories: cubs, subadults and adults. Say that u1 (t) denotes the amount of cubs in year t, u2 (t)
denotes the amount of subadults in year t and uz (t) denotes the amount of adults in year t. Assume the following about the population of pandas:
• Cubs remain cubs for only one year - they have a mortality rate of 15% and the rest become subadults%3;
Approximately 25% of subadults mature to adults each year, approximately 20% of subadults die year year, and the rest remain in this classification;
• On average, adults give birth to 0.5 new cubs each year;
• 95% of adults survive from one year to the next.
We can model the change in class structure each year using the model,
ú(t + 1) = Aú(t)
[u1(t)
u2 (t) | and A is
u3 (t) ]
where u(t)
Number
Number
Number
Number
Number
Number
Number
Number
Number
(To ensure you are marked correct, please ensure you write all entries in the matrix as fractions)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F250d2d05-ac8a-4abf-8add-9b8dedd903f0%2Fe07e7789-a955-49db-94c9-cac5f5570e14%2Fb38j4f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Giant pandas are a vulnerable species famous for their consumption of large amounts of bamboo. Suppose we track the female population of a group of
pandas year-to-year, and classify the pandas into three categories: cubs, subadults and adults. Say that u1 (t) denotes the amount of cubs in year t, u2 (t)
denotes the amount of subadults in year t and uz (t) denotes the amount of adults in year t. Assume the following about the population of pandas:
• Cubs remain cubs for only one year - they have a mortality rate of 15% and the rest become subadults%3;
Approximately 25% of subadults mature to adults each year, approximately 20% of subadults die year year, and the rest remain in this classification;
• On average, adults give birth to 0.5 new cubs each year;
• 95% of adults survive from one year to the next.
We can model the change in class structure each year using the model,
ú(t + 1) = Aú(t)
[u1(t)
u2 (t) | and A is
u3 (t) ]
where u(t)
Number
Number
Number
Number
Number
Number
Number
Number
Number
(To ensure you are marked correct, please ensure you write all entries in the matrix as fractions)
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