Question

Nine-banded armadillos always give birth to quadruplets—four identical babies (called pups). Jenny's armadillo has produced four female pups. Jenny realizes that each of those pups could eventually have four more armadillos. A. How many armadillos would Jenny have if the four pups grew up to have four more pups each? B. What if every generation of Jenny's armadillos was female? How many armadillos would there be if you only count the ones in the 5th generation? Can you write a formula for the number of armadillos in any given generation? Please explain what each variable and each number in your formula means. C. According to this formula the world should be overrun with armadillos after 20 to 25 generations. Why isn't this true in real life?

Answer 1

A.) 85 armadillos

B.) 256 female armadillos

4^(n - 1)

C. Yes. It is true.

Explanation:

Given that armadillo always give birth to quadruplets—four identical babies (called pups).

And Jenny's armadillo has produced four female pups

If Jenny each of those pups eventually have four more armadillos. And if the four pups grew up to have four more pups each, Jenny will have the following,

The first 4 will produce a total of

4×4 = 16 armadillos

Then, 16 armadillos will produce

16×4 = 64 armadillos

Jenny will then have a total of

64 + 16 + 4 + 1 = 85 armadillos

B.) First generation = 1

Second generation = 1 × 4 = 4

Third generation = 4×4 = 16

Fourth generation = 16×4 = 64

Fifth generation = 64×4 = 256

if you only count the ones in the 5th generation, the number will be 256 armadillos

First generation = 4^(n - 1)

Where n = 1

4^0 = 1

Second generation = 4^(n - 1 )

Where n = 2

4^1 = 4

Therefore, a formula for the number of armadillos in any given generation will be 4^( n - 1 )

Where n = number of generation

C.) After 25th generation, the number of armadillos will be

4^(n - 1)

Where n = 25

Substitute 25 for n

4^(25 - 1)

4^24 = 2.8×10^14 armadillos

That is more than 280 trillions armadillos. Whereas, the total number of people in the world population is not upto 10 billions

Therefore, it is true that the world would be overrun with armadillos after 20 to 25 generations