Question

When Paisley moved into a new house, she planted two trees in her backyard. At thetime of planting, Thee A was 21 inches tall and Tree B was 33 inches tall. Each yearthereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. LetA represent the height of Tree At years after being planted and let B represent theheight of Tree Bt years after being planted. Write an equation for each situation, interms oft, and determine the interval of time, t, when Tree A is taller than Tree B.A= 21 + 6t – 6B = 33 + 3t-3Tree A is taller than Tree B whentNote: The interval will only apply for valid values oft in the domainSubmit Answer

Answer 1

Tree A

$A=21+6t$

Tree B

$B=33+3t$

To determine the interval, we must write that A is greater than B with an inequality

$A>B$

OR

$21+6t>33+3t$

and solve t

$\begin{gathered} 6t-3t>33-21 \\ 3t>12 \\ t>\frac{12}{3} \\ t>4 \end{gathered}$

so, the interval is

$(4,\infty)$