solve question d within 10 mins with explanation and get multiple upvotes 1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is500, and that at the start of any subsequent day the number of bees in the hive has increasedby 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 inthe sense that b(t) agrees with the beekeeper's estimates whenever t € N. Here t € Rmeasures the number of days since the start of the year (e.g. t = 1/2 is noon on NewYear's day). Similarly, you should consider the population of bees to be a graduallygrowing 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 inputand outputting the population of bees in the hive at that time. Provide a similardescription for what the function b-¹ does.(e) Find the derivative b'(t). Explain what b'(t) is measuring by giving a description of thesame type that you gave in part (d).(f) On which date does the population of bees in the hive reach 10000? Suppose that at theend 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 hivethroughout 2019, given the migration described in (f). Assume that the populationcontinues 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?

We need to describe the equation of b-1 in words.

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.