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. (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 6-¹ does.
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. (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 6-¹ does.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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