Question

The number of weeds in a yard are on a rise due to recent rains. There were intially 30 weeds in the yard, and each day 5 more appear. a.) write an equation to model the situation. b). How many days will it take to reach 100 weeds in the yard.

Answer 1

Explanation

Algebra / Linear Equations / Linear Equations in the Real World / Applications Using Linear Models

From the statement, we know that:

• there are initially y₀ = 30 weeds in a yard,

,

• each day 5 more weeds appear, so the rate of change is m = 5 weeds/day.

a) Defining the variable x for the number of days, and y for the number of weeds, we have:

$y=y_0+m\cdot x=30\text{ weeds}+5\cdot\text{ weeds/day}\cdot x.$

Or simply we can write:

$y=30+5x.$

b) We want to know how many days (x) we need to have y = 100 weeds in the yard. So we must solve for x the equation:

$100=30+5x.$

Solving for x, we get:

$\begin{gathered} 5x=100-30, \\ 5x=70, \\ x=\frac{70}{5}=14. \end{gathered}$Answer

a) The equation to model the situation is:

$y=5x+30$

b) We need 14 days to reach 100 weeds in the yard.