Question

A landscaper planted 10 cattails by a new pond. The number of cattails double each month over a period of time. Write a function f(x) to model the number of cattails in the pond after x months. f(x)=?

Answer 1

Answer:

$\large \boxed{f(x) = 10(2)^{ x}}$

Step-by-step explanation:

Write a table giving the number of cattails for the first few months

$\begin{array}{lr}\mathbf{x} & \mathbf{f(x)}\qquad \qquad\quad \\0 & 10 = 2^{0}(10) = 10(2)^{0}\\1 & 2(10) = 2^{1}(10)= 10(2)^{1} \\2 & 2\times2(10) = 2^{2}(10)= 10(2)^{2} \\3 & 2\times 2^{2}(10) = 2^{3}(10)= 10(2)^{3}\\4 & 2\times 2^{3}(10) = 2^{4}(10)= 10(2)^{4}\\\end{array}\\\text{The pattern appears to be \large \boxed{\mathbf{f(x) = 10(2)^{\mathbf{x}}}} }$