Question

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

Answer 1

Ques 1)

C) an exponential.

Ques 2)

B) be around 160

Explanation:

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:

`y=3.9926e^(0.1141x)`

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

Hence,

`y=3.9926* e^(0.1141* 32)\\\\y=3.9926* 38.5208633611\\\\y=153.7984`

Hence, the correct answer is:

B)be around 160