Acell of some bacteria divides into two cells every 10 minutes. the initial population is 3 bacteria. (a) find the size of the population after t hours (function of t) (b) find the size of the population after 7 hours. # preview | preview (c) when will the population reach 21? t42 preview

(a)

(b)

(c) 28.07 minutes

Step-by-step explanation:

A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.

That means sequence formed will be 3, 6, 12, 24............

We can easily say that this sequence is a geometric sequence having common ratio (r) =

r = 2

Now we know the explicit formula of a geometric sequence is given by

Where a = Initial population = 3 bacteria

r = common ratio = 2

and t = time in hours

So explicit formula will be

(a) Now we have to calculate the size of population after t hours

(b) We have to find the size of population after 7 hours or 420 minutes

=

After 7 hours bacteria population will be

(c) Time to reach population as 21

By the explicit formula

Now we take log on both the sides of the equation

6t log2 = log 7

6t(0.301) = 0.845

t(1.806) = 0.845

t = hours

Or t = 0.468×60 = 28.07 minutes

Therefore, after 28.07 minutes bacterial population will be 21

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have