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

Step-by-step explanation:

Given: A population of geese grow in such a way that each generation is simply 2.2 times the previous generation. It means they grow exponentially.

The initial number of geese in the first generation = 3

The exponential growth equation for nth generation is given by :-

$y=Ab^{n-1}$, where A is the initial amount and b is the multiplicative rate of change.

such that  for n=1, $y=3(2.2)^{1-1}=3$

In 15th generation with multiplicative rate of change b= 2.2, the population is given by :-

$y=3(2.2)^{15-1}\\\Rightarrow\ y=3(62218.21)\\\Rightarrow\ y=186654.63\approx186655$

Answer 2

This would produce a geometric sequence of the form:

g=3(2.2)^(n-1)

The sum of which is:

g=3(1-2.2^n)/(1-2.2) cleaning up a bit...

g=-3.6(1-2.2^n)

g(15)=-3.6(1-2.2^15)

g(15)=492764.6, since the number of geese must be an integer...

g(15)=492764