Suppose a particular insect came into the United States and, by the time it was discovered at the end of 2016, its population was estimated to be 2,000. Scientists note that the number of insects continually increases by 15% each month. Given the following formula to represent the situation, answer the following questions: N(t)= the number of insects after t months N(t) = N.ert Næ the initial number of insects r= rate of growth %3D t= time in months a. Use the information above to write a function to represent the number of insects present after t months. b. Assuming the growth remains continuous, how many insects will there be at the end of 2018? Show your work! (Hint: Let t = # of months from 2016-2018) Calculations:
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Answer the questions in the screen shot
![Suppose a particular insect came into the United States and, by the time it was discovered at the end of
2016, its population was estimated to be 2,000. Scientists note that the number of insects continually
increases by 15% each month.
Given the following formula to represent the situation, answer the following questions:
N(t)= the number of insects after t months
N(t) = N,ert N# the initial number of insects
r= rate of growth
t= time in months
a. Use the information above to write a function to represent the number of insects
present after t months.
b. Assuming the growth remains continuous, how many insects will there be at the end of 2018?
Show your work! (Hint: Let t = # of months from 2016-2018)
Calculations:
Answer the question in a complete sentence:
c. Assuming the growth remains continuous, when will the number of insects reach one million?
Show your calculations or graphs, then state your answer as the month and year.
(HInt: Use the formula given to plug in your values then solve for t using logs. )
Calculations:
Answer the question in a complete sentence: (State your solution for t then figure out the
month and year past the end of 2016)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F457f10bb-da69-48b8-9913-b9abb1ef9f07%2F91bd01c3-4399-4561-b142-c2a8629a22b8%2F7q868p_processed.png&w=3840&q=75)
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