Answer:
6926 pairs in 2016.
Step-by-step explanation:
The number of pairs in t years after 2010 is modeled by the following function:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the number of pairs in 2010 and r is the growth rate, as a decimal.
608 pairs in 2010
This means that [tex]P(0) = 608[/tex]
So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]P(t) = 608(1+r)^{t}[/tex]
4617 pairs five year later.
So P(5) = 4617. We use this to find 1 + r.
[tex]P(t) = 608(1+r)^{t}[/tex]
[tex]4617 = 608(1+r)^{5}[/tex]
[tex](1+r)^{5} = \frac{4617}{608}[/tex]
[tex]1 +r = \sqrt[5]{\frac{4617}{608}}[/tex]
[tex]1 + r = 1.5[/tex]
So
[tex]P(t) = 608(1.5)^{t}[/tex]
How many pairs in 2016?
2016 is 2016 - 2010 = 6 years after 2010. So this is P(6).
[tex]P(t) = 608(1.5)^{t}[/tex]
[tex]P(6) = 608(1.5)^{6} = 6926[/tex]
6926 pairs in 2016.
