Question

The sequence shows the population of ducks on an island after 1,2,3 and 4 years. 4,24,144,864 if the pattern continues which function could be used to find the population of ducks after n years

Answer 1

p(n) = 4·6^(n-1)

Explanation:

The sequence is a geometric sequence with first term 4 and common ratio ...

24/4 = 144/24 = 864/144 = 6

The general term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

Filling in the values for this sequence, we have the general term ...

an = 4·6^(n-1)

Putting this in functional form, we have the population p as a function of year n ...

p(n) = 4·6^(n-1)