Question

A population of geese grow in such a way that each generation is simply 2.2 times the previous generation. There were 3 geese in the first generation, how many will there be by the 15th generation?

Answer 1

Answer:

186655 geese

Step-by-step explanation:

In this question , the next generation is calculated by multiplying the current generation by 2.2. Let's do a simple math;

1st generation = 3

2nd generation= 3×2.2=6.6

3rd generation=6.6×2.2=14.52

4th generation=14.52×2.2=31.94

5th generation=31.94×2.2=70.28

6th generation= 70.28×2.2=154.61

7th generation=154.62×2.2=340.14

8th generation=340.14×2.2=748.31

9th generation=748.31×2.2=1646.28

10th generation=1646.28×2.2=3621.81

11th generation=3621.81×2.2=7967.98

12th generation=7967.98×2.2=17529.55

13th generation=17529.55×2.2=38565.0

14th generation=38565.0×2.2=84843.02

15th generation=84843.02×2.2=186654.64

=186655 geese

OR

If current generation is calculated as the previous generation multiplied by a factor then you should see that this is an exponential function.In this case

Original number of geese=3

Factor of multiplication is =2.2

Exponential function for first generation is =0

How? see here

$1st=3*2.2^0=3*1=3\\\\2nd=3*2.2^1=3*2.2=6.6\\\\3rd=3*2.2^2=3*4.84=14.52$

So from the above you can derive an expression for 15th generation

You notice for 1st generation , the exponent is 0

For the 2nd generation the exponent is is 1

For the 3rd generation the exponent is 2

Thus for the nth generation the exponent will be n-1

Your expression for nth generation can now be;

$nth=3*2.2^{n-1}$

For 15th generation

$15th=3*2.2^{15-1} =3*2.2^{14} =186654.63\\\\\\=186655$