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

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

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*2(10) = 2^(2)(10)= 10(2)^(2) \\3 & 2* 2^(2)(10) = 2^(3)(10)= 10(2)^(3)\\4 & 2* 2^(3)(10) = 2^(4)(10)= 10(2)^(4)\\\end{array}\\\text{The pattern appears to be $\large \boxed{\mathbf{f(x) = 10(2)^{\mathbf{x}}}}$}`