The function f(x) to model the number of fish in the pond after x months is given as function f(x) = [tex]5(2)^x[/tex]
Solution:
Given that landscaper puts 5 fish into a new pond
The number of fish doubles each month over a period of time
To find: function f(x) to model the number of fish in the pond after x months
From given information,
Number of fish doubles each month and initially there put 5 fish into pond
Number of fish after 1 month = 5(2)
Number of fish after 2 months = 5(2)(2) = [tex]5^2[/tex]
Number of fish after 3 months = 5(2)(2)(2) = [tex]5^3[/tex]
Number of fish after 4 months = 5(2)(2)(2)(2) [tex]5^4[/tex]
So after "x" months, number of fish in pond is given as,
number of fish in pond = [tex]5(2)^x[/tex]
function f(x) = [tex]5(2)^x[/tex]
Thus the required function is found
Answer:
F(x) = 5 (2)^x-1
Step-by-step explanation:
If the number of fish doubles each month over a period of time, the sequence may thus be expressed as
5, 10, 20, 40....
This is a geometric sequence with 5 as the first term and 2 as the common ratio.
The function f(x) to model the number of fish in the pond after x months may then be expressed as the nth term
F(x) = 5 (2)^x-1
