Question

A plant is 20inches tall. If the plant grows 2h inches each week for the next 4 weeks and h inches for each of the 2 weeks after that, which expressions shows the height of the plant , in inches, after 6 weeks

Answer 1

`20+10h` inches.

Explanation:

We have been given that a plant is 20 inches. The plant grows
`2h` inches each week for the next 4 weeks.

So growth of plant in 4 weeks would be
`2h` times 4 that is
`2h\cdot 4=8h`.

We are also told that the plant grows
`h` inches for each of the 2 weeks after that. The growth of plant in these 2 weeks would be
`2h`.

The total growth of the plant in 6 weeks would be initial height plus growth in 4 week plus growth in next 2 weeks.

`20+8h+2h\Rightarrow 20+10h`

Therefore, the growth of plant in 6 weeks would be
`20+10h` inches.

Answer 2

`y(6,h) = 24 + 8h`

Explanation:

We are given the following in the question:

Height of plant = 20 inches

Growth of plant for next 4 week = 2h inches.

Growth of plant each week after 4 weeks = 2 inches.

Thus, the expression for plant height is given by

`y = 20 + 4(2h) + (w-4)2, w\geq 4\\y =20 + 8h+2w-8, w\geq 4\\y(w,h) = 12 + 8h + 2w\\\text{If }w \leq 4\\y(w,h) = 20 + 4(2h)\\y(w,h) = 20 + 8h`

We have to find the expression for plant's height in 6 weeks.

Putting w = 6, we get,

`y(6,h) = 12 + 8h + 2(6)\\y(6,h) = 24 + 8h`

is the required expression.