To study population growth in rats, a team of researchers placed a few rats on an uninhabited island with very few predators . the table records their observations over 31 days
| day| rat population|
1 , 4
12, ,20
21,43
26,68
28,86
29,105
30,129
31,156
the data shows
a) a postive linear
b)a negative linear
c)an exponential
d)a parabolic
based on the table , we can assume that the rat population on 32nd day will be
a) be around 130
b)be around 160
c)be around 180
d) not change

Ques 1)

C)   an exponential.

Ques 2)

B)   be around 160

Ques 1)

        Day                    rat population|

          1                              4  

         12                           20

         21                           43

        26                          68

        28                          86

        29                         105

       30                          129

       31                           156

Clearly we see that as the number of days increases the population of rat also increases.

Hence, the data shows a positive relationship.

Now we have to check the behavior of the relationship whether the increase is linear, exponential or parabolic.

When we plot these points in a regression calculator we see that the r² value is highest if the trend line is a exponential curve.

Hence, the data is best represented by a exponential curve.

Ques 2)

We get a exponential equation that represent this curve as:

Hence, we are asked to find the value of y when x=32

Hence,

Hence, the correct answer is:

        B)be around 160

area of rectangle a is 2 times that of rectangle b that means 2x+x =   36cm^2

3x = 36cm ^2

x = 36/3

x= 12cm^2

and 2x = 24cm^2

now side of square = are divided by sides = 36/4 = 6cm

that means length of rectangle a and b is 6cm too

now for rectangle a,

l*b = area

= 6*y=24

y=24/6 = 4

therefore dimensions of rectangle a are- length = 6cm, breadth = 4cm

and for rectangle b, length = 6cm and breadth = 6-4 = 2cm.

hope this .

8: 40

2 hours

10: 40

55 min

11: 35