Answer:
[tex]\large \boxed{f(x) = 10(2)^{ x}}[/tex]
Step-by-step explanation:
Write a table giving the number of cattails for the first few months
[tex]\begin{array}{lr}\mathbf{x} & \mathbf{f(x)}\qquad \qquad\quad \\0 & 10 = 2^{0}(10) = 10(2)^{0}\\1 & 2(10) = 2^{1}(10)= 10(2)^{1} \\2 & 2\times2(10) = 2^{2}(10)= 10(2)^{2} \\3 & 2\times 2^{2}(10) = 2^{3}(10)= 10(2)^{3}\\4 & 2\times 2^{3}(10) = 2^{4}(10)= 10(2)^{4}\\\end{array}\\\text{The pattern appears to be $\large \boxed{\mathbf{f(x) = 10(2)^{\mathbf{x}}}}$}[/tex]
