When Alexander moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each

year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per

year. Let A represent the height of Tree At years after being planted and let B

represent the height of Tree Bt years after being planted. Write an equation for each

situation, in terms of t, and determine which tree is taller after 3 years.

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Step-by-step explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per  year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

∴ A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

∴ B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

if you was gonna solve for a, a is a   < -12