# Probability, population growth, and interest

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1) A bacteria culture starts with 7 bacteria which multiply simultaneously every three house. If the first generation is born fromt he initial group at 12 midnight

a. How many bacteria will be in the culture at midnight the next night?

b. Also what time will there be 224 bacteria in the culture?

2) If you put $85.00 in a 4% single interest account that applies interest annually

a. How much will you have after 10 years?

b. In how many years will you have $153.00 in the account?

3) For the data set 2,-4,11,2,4 find the following

a. Mean

b. Median

c. Mode

d. Range

e. Standard deviation

4) Find the probability of tossing a "face divisible by 3" in a roll of dice

5) Find the probability of tossing an "even face" following by a "5" on two rolls of a dice

#### Solution Preview

1) A BACTERIA CULTURE STARTS WITH 7 BACTERIA WHICH MULTIPLY

SIMULTANEOUSLY EVERY THREE HOURS.IF THE FIRST GENERATION IS BORN

FROM THE INITIAL GROUP AT 12 MIDNIGHT. (A) HOW MANY BACTERIA WILL BE IN THE

CULTURE AT MIDNIGHT THE NEXT NIGHT? (B) ALSO WHAT TIME WILL THERE BE

224 BACTERIA IN THE CULTURE?

how many generations until midnight next? 12, 3, 6, 9, 12, 3, 6, 9, 12 nine generations

what happens at each generation...first generation 7 x 2 = 14

second generation 7 x 2^2 = 28

third generation 7 x 2^3 = 56 and so on ...

so for each generation n we have 7 x 2^n bacteria in the culture.

How many generations did we say until 12 the next night ....nine so we have 7 x 2^9 beasties.

Here, of course we are assuming none die or have other reproductive problems.

Ok and now we have a number of beasties that can also be given by our formula 7 x 2^n = 224 bacteria

so factor out 7 first leaving 32 and

then how many factors of two is 32 =2 x 16 = 2 x 2 x 8= 2 x 2 x 2 x 4 = 2^5 so 5 generations counting from 12 midnight that is 12, 3, 6, 9, 12 Noon. So at 12 noon until 2:59:99.99999999 PM we will expect to have 224 bacteria swimming happily in our media for their growth.

2) IF YOU PUT 85.00 DOLLARS IN A 4% SINGLE INTEREST ACCOUNT THAT APPLIES

INTEREST ...

#### Solution Summary

Topics in this problem set include interest, mean, median, mode, range, standard deviation, population growth, and probability.