1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is 500, and that at the start of any subsequent day the number of bees in the hive has increased by 1% compared to what it was exactly one day earlier. (a) Find a function b: R→ (0, ∞) such that b(t) models the population of the hive in the sense that b(t) agrees with the beekeeper's estimates whenever te N. Here tER measures the number of days since the start of the year (e.g. t = 1/2 is noon on New Year's day). Similarly, you should consider the population of bees to be a gradually growing real number (ignore the fact that it is actually restricted to being an integer). (b) Explain why the inverse function b-¹ exists. (c) Calculate a formula for b-¹.
1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is 500, and that at the start of any subsequent day the number of bees in the hive has increased by 1% compared to what it was exactly one day earlier. (a) Find a function b: R→ (0, ∞) such that b(t) models the population of the hive in the sense that b(t) agrees with the beekeeper's estimates whenever te N. Here tER measures the number of days since the start of the year (e.g. t = 1/2 is noon on New Year's day). Similarly, you should consider the population of bees to be a gradually growing real number (ignore the fact that it is actually restricted to being an integer). (b) Explain why the inverse function b-¹ exists. (c) Calculate a formula for b-¹.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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solve question a,b,c asap within 10 mins with explanation
![1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is
500, and that at the start of any subsequent day the number of bees in the hive has increased
by 1% compared to what it was exactly one day earlier.
(a) Find a function b : R → (0, ∞) such that b(t) models the population of the hive in
the sense that b(t) agrees with the beekeeper's estimates whenever t € N. Here t € R
measures the number of days since the start of the year (e.g. t = 1/2 is noon on New
Year's day). Similarly, you should consider the population of bees to be a gradually
growing real number (ignore the fact that it is actually restricted to being an integer).
(b) Explain why the inverse function b-¹ exists.
(c) Calculate a formula for 6-¹.
(d) The function b can be described as taking the time since the start of this year as input
and outputting the population of bees in the hive at that time. Provide a similar
description for what the function b-¹ does.
(e) Find the derivative b'(t). Explain what b'(t) is measuring by giving a description of the
same type that you gave in part (d).
(f) On which date does the population of bees in the hive reach 10000? Suppose that at the
end of that day all but 1000 of the bees leave the hive to start a new colony elsewhere.
(g) Write a function c: [0, 365] → (0, ∞) which gives the population of bees in the hive
throughout 2019, given the migration described in (f). Assume that the population
continues to increase at the same rate (1% per day) after the migration.
(h) What is the population of bees in the hive at the end of the year?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c6be440-ec16-4c88-9306-17cfd017b9da%2Fb4f5a381-0cf0-4f51-8ba9-7359accf63a3%2Ffrg11vg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is
500, and that at the start of any subsequent day the number of bees in the hive has increased
by 1% compared to what it was exactly one day earlier.
(a) Find a function b : R → (0, ∞) such that b(t) models the population of the hive in
the sense that b(t) agrees with the beekeeper's estimates whenever t € N. Here t € R
measures the number of days since the start of the year (e.g. t = 1/2 is noon on New
Year's day). Similarly, you should consider the population of bees to be a gradually
growing real number (ignore the fact that it is actually restricted to being an integer).
(b) Explain why the inverse function b-¹ exists.
(c) Calculate a formula for 6-¹.
(d) The function b can be described as taking the time since the start of this year as input
and outputting the population of bees in the hive at that time. Provide a similar
description for what the function b-¹ does.
(e) Find the derivative b'(t). Explain what b'(t) is measuring by giving a description of the
same type that you gave in part (d).
(f) On which date does the population of bees in the hive reach 10000? Suppose that at the
end of that day all but 1000 of the bees leave the hive to start a new colony elsewhere.
(g) Write a function c: [0, 365] → (0, ∞) which gives the population of bees in the hive
throughout 2019, given the migration described in (f). Assume that the population
continues to increase at the same rate (1% per day) after the migration.
(h) What is the population of bees in the hive at the end of the year?
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