Question

Jamie is measuring the growth of a bean plant in her garden. On the first day, the plant is 2.5 inches tall. On the fourth on the ninth day, it is 14.5 inches tall. What will be the height of Jamie’s plant in the twenty-first day if it continues to

Answer 1

82.5 feet.

Explanation:

Let x represent number of days and y represent height of the plant.

We have been given that Jamie is measuring the growth of a bean plant in her garden. On the first day, the plant is 2.5 inches tall. Point (1,2.5) represent this situation.

On the fourth day, it is 14.5 inches tall. This information can be represented by point (4,14.5).

Let us find slope of the line using given points.

`m=(y_2-y_1)/(x_2-x_1)`

`m=(14.5-2.5)/(4-1)`

`m=(12)/(3)`

`m=4`

Now, we will point-slope form of equation to find the equation for the height of the plant.

`(y-y_1)=m(x-x_1)`

`(y-2.5)=4(x-1)`

`y-2.5=4x-4`

`y-2.5+2.5=4x-4+2.5`

`y=4x-1.5`

Now, we will substitute
`x=21` in our equation.

`y=4(21)-1.5`

`y=84-1.5`

`y=82.5`

Therefore, the height of Jamie’s plant will be 82.5 feet on the twenty-first day if it continues to grow.