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Darya [45]
2 years ago
10

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate

parameter of 1.5% per hour. How many hours does it take for the size of the sample to double
Mathematics
1 answer:
KonstantinChe [14]2 years ago
7 0

Answer:

It will take 47 hours

Step-by-step explanation:

We can have the exponential function as follows;

P = I( 1 + r)^n

if the initial value was x , the final will be 2x

The change rate is 1.5% , which is r, this is same as;

1.5/100 = 0.015

So what we want to calculate is the n attached

This will be;

2x = x ( 1 + 0.015)^n

2 = 1.015^n

ln 2 = n ln 1.015

n = ln 2/ln 1.015

n = 46.55

This is approximately 47 hours

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How many permutations are there of the letters in the words (a) TRISKAIDEKAPHOBIA (fear of the number 13)? (b) FLOCCINAUCINIHILI
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Answer: Hello!

Let's start with the word TRISKAIDEKAPHOBIA wich has 17 letters (some of them repeat, but it does not matter in this problem)

We want to know how many permutations we can do with 17 letters: then think this way, Lets compose a word. The first letter of this word has 17 options, the second letter of the word has 16 options (you already took one of the set) the third letter of the word has 15 options, and so on.

The total number of permutations is the product of the number of options that you have for each letter, this is:

17*16*15*14*....*3*2*1 = 17! = 3.6e+14

(b) FLOCCINAUCINIHILIPILIFICATION now we have 30 letters in total, using the same reasoning as before, here we have 30! permutations; this is

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(c) PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS: now there are 47 letters.

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