When Cameron moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 24 inches tall and Tree B was 39 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t, t, and determine the interval of time, t, t, when Tree A is taller than Tree B.

time interval when Tree A is taller than Tree B is;

t > 5 years

Step-by-step explanation:

Tree A;

Initial height = 24 inches

Increase in height per year = 6 inches per year

Thus, for t years after being planted, height is;

A = 6t + 24

Tree B;

Initial height = 39 inches

Increase in height per year = 3 inches per year

Thus, for t years after being planted, height is;

B = 3t + 39

For tree A to be taller than tree B, then it means thay;

A > B

Thus;

6t + 24 > 3t + 39

Subtract 3t from both sides to get;

6t - 3t + 24 > 39

3t + 24 > 39

3t > 39 - 24

3t > 15

Divide both sides by 3 to get;

t > 5

Thus, time interval when Tree A is taller than Tree B is; t > 5

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x